From ebd2d17125ac32810a59bf3a7f6b9b453b3f6720 Mon Sep 17 00:00:00 2001 From: "Oriol (Prodesk)" Date: Thu, 31 Oct 2019 02:08:18 +0100 Subject: [PATCH 1/6] start updating and rewriting schema.md --- schema.md | 119 +++++++++++++++++++++++++----------------------------- 1 file changed, 54 insertions(+), 65 deletions(-) diff --git a/schema.md b/schema.md index da83289122..ae3a42a324 100644 --- a/schema.md +++ b/schema.md @@ -1,82 +1,71 @@ -# Design for netcdf storage format for mcmc traces +# InferenceData schema specification +The `InferenceData` schema scheme defines a data structure compatible with [NetCDF](https://www.unidata.ucar.edu/software/netcdf/) with 3 goals in mind, usefulness in the analysis of Bayesian inference results, reproducibility of Bayesian inference analysis and interoperability between different inference backends and programming languages. -/ -All data relating to a mcmc run. +Currently there are 2 implementations of this design: +* [ArviZ](https://arviz-devs.github.io/arviz/) in Python which integrates with: + - [emcee](https://emcee.readthedocs.io/en/stable/) + - [PyMC3](https://docs.pymc.io) + - [pyro](https://pyro.ai/) + and [numpyro](https://pyro.ai/numpyro/) + - [PyStan](https://pystan.readthedocs.io/en/latest/index.html), + [CmdStan](https://mc-stan.org/users/interfaces/cmdstan) + and [CmdStanPy](https://cmdstanpy.readthedocs.io/en/latest/index.html) + - [tensorflow-probability](https://www.tensorflow.org/probability) +* [ArviZ.jl](https://github.com/sethaxen/ArviZ.jl) in julia which integrates with: + - [Turing](https://turing.ml/dev/). -attrs: -backend: "stan" or "pymc3" -version: str -model_name?: str -comment?: str -model_version?: str -timestamp: int -author?: str +## Current design +`InferenceData` stores all quantites relevant in order to fulfill its goals in different groups. Each group, described below, stores a conceptually different quantity generally represented by several multidimensional labeled variables. -/coords -For each dimension, we store a corresponding variable here, that contains the labels for that dimension. +Each group should have one entry per variable, with the first two dimensions of each variable should be the sample identifier (`chain`, `draw`). Dimensions must be named and explicit their index values, called coordinates. Coordinates can have repeated identifiers and may not be numerical. Variable names must not share names with dimensions. -/model -Each backend can store a representation of the model in here. (I guess -source code for stan, no clue for pymc3 at this point.) +Moreover, each group contains the following attributes: +* `created_at`: the date of creation of the group. +* `inference_library`: the library used to run the inference. +* `inference_library_version`: version of the inference library used. -/sample_stats -Statistics computed while sampling, like step size (step_size), depth, diverging, energy (for HMC), log probability (lp), and log likelihood (log_likelihood). +`InferenceData` data objects contain any combination the groups described below. -/initial_point - One point in parameter space for each chain, where that chain started. - TODO We could also store that as an attribute to each var in /trace +#### `posterior` +Samples from the posterior distribution p(theta|y). -/tuning_trace? - Same as /trace, but optional. It contains the trace during tuning. Optional. (only if store_tune=True or so?) +#### `sample_stats` +Information and diagnostics about each `posterior` sample, provided by the inference backend. It may vary depending on the algorithm used by the backend (i.e. an affine invariant sampler has no energy associated). The name convention used for `sample_stats` variables is the following: +* `lp`: unnormalized log probability of the sample +* `step_size` +* `step_size_bar` +* `tune`: boolean variable indicating if the sampler is tuning or sampling +* `depth`: +* `tree_size`: +* `mean_tree_accept`: +* `diverging`: HMC-NUTS only, boolean variable indicating divergent transitions +* `energy`: HMC-NUTS only +* `energy_error` +* `max_energy_error` -/tuning_advi? - Some data about an initialization advi run? History of convergence stats, final sd and mu params? Optional +#### `observed_data` +Observed data on which the `posterior` is conditional. It should only contain data which is modeled as a random variable. Each variable should have a counterpart in `posterior_predictive`. The `posterior_predictive` counterpart variable may have a different name. -/divergences - Points in parameter space where the leapfrog starts that lead to a divergence (excluding tuning). - Does stan have access to that info? We could also just store the accepted point of a divergent trajectory. +#### `posterior_predictive` +Posterior predictive samples p(y|y) corresponding to the posterior predictive pdf evaluated at the `observed_data`. Samples should match with `posterior` ones and each variable should have a counterpart in `observed_data`. The `observed_data` counterpart variable may have a different name. -/observed_data - All data that is used in observed variables (or the data (or transformed?) data sections in stan.) +#### `constant_data` +Model constants, data included in the model which is not modeled as a random variable (i.e. the x in a linear regression). It should be the data used to generate the `posterior` and `posterior_predictive` samples. -/warnings - A list of warnings during sampling. Eg low effective_n, divergences.... - TODO Not sure about the format. Can we somehow share at least part of that between stan/pymc? - They mostly produce the same warnings I think. +#### `prior` +p(theta) -/prior? -Samples from the prior distribution. Same shapes as in trace. (except for (sample, chain)) +#### `sample_stats_prior` -/prior_predictive? -Samples from the prior predictive distribution. Same vars as in /data +#### `prior_predictive` -/posterior_predictive? -Samples from the posterior predicitve distribution. Same vars as in /data +## Planned features -/trace -TODO We could call this /posterior +### Sampler parameters - attrs: - The final parameters for the sampler. ie the final mass matrix and step size. +### Out of sample posterior_predictive samples +#### `predictions` +Out of sample posterior predictive samples p(y'|y). - /trace//var1 - One entry for each variable. The first two dimensions should always be - `(chain, sample)`. I guess the decision whether or not we want to expose a stacked version `draw=('chain', 'sample')` - is up to arviz. - - Variable names must not share names with coordinate names. - - attrs: - is_free: Whether or not the variable is a free variable for the sampler, or a transformed one - domain: One of (“reals”, “pos-reals”, “integers”, “sym-pos-def”, "interval"...) - TODO For stuff like sym-pos-def we need to know along which dims it is a matrix. - TODO This data could also be stored in /model - sym_pos_axis: [dim_idx1, dim_idx2] - interval_lower: - interval_upper - TODO How would this deal with cases where the lower and upper bounds depend on the index? - - - -TODO: In order to reproduce the run, it may make sense to also store some data on the random state (in numpy, this is a tuple of arrays), as -well as some version info. Hopefully just `PyMC3, (3, 4, 1)` or similar works. +#### `constant_data_predictions` +Model constants used to get the `predictions` samples. Its variables should have a counterpart in `constant_data`. From 2dba7f8d9869926cc96272e1bab291965b2e263d Mon Sep 17 00:00:00 2001 From: Oriol Abril Date: Sat, 2 Nov 2019 17:50:06 +0100 Subject: [PATCH 2/6] fix typo in quantities Co-Authored-By: Seth Axen --- schema.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/schema.md b/schema.md index ae3a42a324..7d86200adc 100644 --- a/schema.md +++ b/schema.md @@ -15,7 +15,7 @@ Currently there are 2 implementations of this design: - [Turing](https://turing.ml/dev/). ## Current design -`InferenceData` stores all quantites relevant in order to fulfill its goals in different groups. Each group, described below, stores a conceptually different quantity generally represented by several multidimensional labeled variables. +`InferenceData` stores all quantities relevant in order to fulfill its goals in different groups. Each group, described below, stores a conceptually different quantity generally represented by several multidimensional labeled variables. Each group should have one entry per variable, with the first two dimensions of each variable should be the sample identifier (`chain`, `draw`). Dimensions must be named and explicit their index values, called coordinates. Coordinates can have repeated identifiers and may not be numerical. Variable names must not share names with dimensions. From 6b9b7f040a6d5ae12421696bf3a4e90855257b5e Mon Sep 17 00:00:00 2001 From: Oriol Abril Date: Sat, 2 Nov 2019 17:58:57 +0100 Subject: [PATCH 3/6] Capitalize Julia Co-Authored-By: Colin --- schema.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/schema.md b/schema.md index 7d86200adc..d5625ff8f5 100644 --- a/schema.md +++ b/schema.md @@ -11,7 +11,7 @@ Currently there are 2 implementations of this design: [CmdStan](https://mc-stan.org/users/interfaces/cmdstan) and [CmdStanPy](https://cmdstanpy.readthedocs.io/en/latest/index.html) - [tensorflow-probability](https://www.tensorflow.org/probability) -* [ArviZ.jl](https://github.com/sethaxen/ArviZ.jl) in julia which integrates with: +* [ArviZ.jl](https://github.com/sethaxen/ArviZ.jl) in Julia which integrates with: - [Turing](https://turing.ml/dev/). ## Current design From e76738c2910554fe5ba5ed1a581e99fdc93f89e2 Mon Sep 17 00:00:00 2001 From: "Oriol (Prodesk)" Date: Sun, 10 Nov 2019 22:02:13 +0100 Subject: [PATCH 4/6] add pystan schema example --- schema/PyStan_schema_example.ipynb | 5265 ++++++++++++++++++++++++++++ schema/linear_regression_data.csv | 6 + 2 files changed, 5271 insertions(+) create mode 100644 schema/PyStan_schema_example.ipynb create mode 100644 schema/linear_regression_data.csv diff --git a/schema/PyStan_schema_example.ipynb b/schema/PyStan_schema_example.ipynb new file mode 100644 index 0000000000..4c49ffd920 --- /dev/null +++ b/schema/PyStan_schema_example.ipynb @@ -0,0 +1,5265 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Example of `InferenceData` schema in PyStan\n", + "The description of the `InferenceData` structure can be found in [GitHub](https://github.com/arviz-devs/arviz/blob/master/schema.md)." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import arviz as az\n", + "import pystan\n", + "import pandas as pd\n", + "import numpy as np\n", + "import xarray\n", + "xarray.set_options(display_style=\"html\")" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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Alice75004.5
Bob101006.0
Cole186007.0
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Erika2750018.0
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" + ], + "text/plain": [ + " comments time\n", + "Alice 7500 4.5\n", + "Bob 10100 6.0\n", + "Cole 18600 7.0\n", + "Danielle 29200 12.0\n", + "Erika 27500 18.0" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "#read data\n", + "data = pd.read_csv(\"linear_regression_data.csv\", index_col=0)\n", + "time_since_joined = data.time.values\n", + "slack_comments = data.comments.values\n", + "names = data.index.values\n", + "N = len(names)\n", + "data" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "linreg_code = \"\"\"\n", + "data {\n", + " int N;\n", + " real time_since_joined[N];\n", + " real slack_comments[N];\n", + "}\n", + "\n", + "parameters {\n", + " real b0;\n", + " real b1;\n", + " real log_sigma;\n", + "}\n", + "\n", + "transformed parameters {\n", + " real sigma;\n", + " sigma = exp(log_sigma);\n", + "}\n", + "\n", + "model {\n", + " b0 ~ normal(0,10);\n", + " b1 ~ normal(0,10);\n", + " for (i in 1:N) {\n", + " slack_comments[i] ~ normal(b0 + b1 * time_since_joined[i], sigma);\n", + " }\n", + " \n", + "}\n", + "\n", + "generated quantities {\n", + " vector[N] log_lik;\n", + " vector[N] slack_comments_hat;\n", + " for (i in 1:N) {\n", + " log_lik[i] = normal_lpdf(slack_comments[i] | b0 + b1 * time_since_joined[i], sigma);\n", + " slack_comments_hat[i] = normal_rng(b0 + b1 * time_since_joined[i], sigma);\n", + " }\n", + "}\n", + "\"\"\"\n", + "linreg_data_dict = {\"N\": N, \"slack_comments\": slack_comments, \"time_since_joined\": time_since_joined}" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "INFO:pystan:COMPILING THE C++ CODE FOR MODEL anon_model_436a47b6d0471232cc823b9d65bd2bd6 NOW.\n" + ] + } + ], + "source": [ + "sm = pystan.StanModel(model_code=linreg_code)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "prior = sm.sampling(data=linreg_data_dict, iter=200, chains=1, algorithm='Fixed_param', warmup=0)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "posterior = sm.sampling(data=linreg_data_dict, iter=200, chains=4)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "idata_stan = az.from_pystan(\n", + " posterior=posterior,\n", + " prior=prior,\n", + " posterior_predictive=\"slack_comments_hat\",\n", + " prior_predictive=\"slack_comments_hat\",\n", + " observed_data=[\"slack_comments\"],\n", + " constant_data=[\"time_since_joined\"],\n", + " log_likelihood=\"log_lik\",\n", + " coords={\"developer\": names},\n", + " dims={\n", + " \"slack_comments\": [\"developer\"],\n", + " \"log_lik\": [\"developer\"],\n", + " \"slack_comments_hat\": [\"developer\"],\n", + " \"time_since_joined\": [\"developer\"],\n", + " }\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Inference data with groups:\n", + "\t> posterior\n", + "\t> sample_stats\n", + "\t> posterior_predictive\n", + "\t> prior\n", + "\t> sample_stats_prior\n", + "\t> prior_predictive\n", + "\t> observed_data\n", + "\t> constant_data" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "idata_stan" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this example, each variable has as dimension a combination of the following 3: `chain`, `draw` and `developer`. Moreover, each dimension has specific coordinate values. In the case of `chain` and `draw` it is an integer identifier starting at `0`; in the case of `developer` dimension, its coordinate values are the following strings: `[\"Alice\", \"Bob\", \"Cole\", \"Danielle\", \"Erika\"]`." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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      +       "        -1.46931252e-01,  2.55388814e-01,  7.35719362e+00,\n",
      +       "         1.21676225e+01,  1.41360141e+01,  1.41296599e+01,\n",
      +       "         1.41649206e+01,  1.54777632e+01,  1.75734916e+01,\n",
      +       "         1.72502915e+01, -1.77987725e+01, -1.46466181e+01,\n",
      +       "        -1.46549147e+01,  1.03280323e+01,  1.04365548e+01,\n",
      +       "        -1.72113295e+01, -4.62443059e+00, -5.05212854e+00,\n",
      +       "         1.66714307e+01,  2.11717021e+01, -1.41688891e+01,\n",
      +       "        -8.84818236e+00, -9.26781263e+00, -4.64106296e+00,\n",
      +       "        -2.84670585e+00, -2.99076212e+01,  3.32959335e+01,\n",
      +       "        -7.95568615e+00, -6.34101490e+00,  2.38262690e+00,\n",
      +       "         2.72647418e+00,  3.01739313e+00,  3.07701151e+00,\n",
      +       "         3.69893220e+00,  1.08213206e+01,  6.13314050e+00,\n",
      +       "        -2.92417665e+00, -2.46161723e+00, -2.36560216e+00,\n",
      +       "        -2.95842306e+00, -2.79282016e+00, -6.55697652e+00,\n",
      +       "        -4.68357413e+00, -7.24199699e+00, -6.70826056e+00,\n",
      +       "        -3.75928690e+00, -4.16820180e+00, -2.19554375e+01,\n",
      +       "         1.79293402e+01,  6.14510012e+00, -1.34717078e+00,\n",
      +       "        -1.32079690e+00,  1.15105364e+01,  2.57618679e+00,\n",
      +       "         3.03406971e+00,  7.44984950e+00,  5.27284207e+00,\n",
      +       "         5.63957421e+00,  9.75660989e+00,  1.02561615e+01,\n",
      +       "        -2.95407807e+00, -7.42841612e+00, -9.42702998e+00,\n",
      +       "        -9.07218109e+00, -5.38092326e+00, -1.44659933e+01,\n",
      +       "         6.65763639e+00,  1.66563705e+01,  2.13081041e+00,\n",
      +       "        -1.64226034e+00, -1.55012670e+00,  5.58031271e+00,\n",
      +       "         5.14300097e+00,  7.48016510e+00,  7.80352450e+00,\n",
      +       "         2.10484910e+01,  2.10499725e+01,  2.16516147e+01,\n",
      +       "         2.21284050e+01,  2.17925001e+01,  2.22137375e+01,\n",
      +       "         5.02356733e+00,  1.34450493e+01,  1.37574580e+01,\n",
      +       "         1.35390722e+01,  1.12659255e+01,  1.25503569e+01,\n",
      +       "         6.41387284e+00, -1.00451563e+00, -1.36941583e+01,\n",
      +       "        -9.98872813e+00, -9.67945477e+00, -5.48849477e-01,\n",
      +       "        -7.41785465e+00],\n",
      +       "       [ 5.43012676e+00,  9.18158341e+00,  7.19273421e+00,\n",
      +       "        -1.80998716e+01, -8.89809678e+00,  2.00195184e+00,\n",
      +       "         7.86367052e+00,  8.53484192e+00, -9.41513865e+00,\n",
      +       "        -9.44390801e+00,  1.43770510e+01,  3.68103482e+00,\n",
      +       "        -4.71274474e+00, -8.77682219e+00,  2.38828378e+01,\n",
      +       "         1.16260959e+01,  1.90699303e+01, -9.87799485e+00,\n",
      +       "        -4.37807273e+00,  5.58774669e-02,  5.58774669e-02,\n",
      +       "        -6.97899019e-01, -8.21646946e-01, -8.48798586e-01,\n",
      +       "        -1.48517794e+00, -6.26840614e+00, -6.06506208e+00,\n",
      +       "        -5.04492430e+00, -4.72537182e+00, -5.72460762e+00,\n",
      +       "        -1.64592392e+01, -1.43187774e+01,  4.74484386e+00,\n",
      +       "         1.47031257e+01,  5.26185146e-01, -3.55463983e-01,\n",
      +       "         3.70183860e+00,  4.42598265e-01,  3.39639796e-01,\n",
      +       "         6.44894705e-01,  7.28232577e-01,  3.11878077e+00,\n",
      +       "         1.14537228e+01,  1.21356274e+01,  4.56554315e+00,\n",
      +       "         4.54034390e+00, -5.30595940e+00, -5.31548741e+00,\n",
      +       "        -5.26099416e+00, -5.40088952e+00, -6.37066507e+00,\n",
      +       "        -3.41483023e+00, -2.38048318e+01, -2.38045450e+01,\n",
      +       "         3.61216330e+00,  3.72298202e+00,  4.47199992e+00,\n",
      +       "         5.43692421e+00,  4.33791132e+00, -7.76382485e-01,\n",
      +       "        -1.07402321e+00,  1.95684466e+00,  6.09333620e+00,\n",
      +       "         7.01859748e-01, -4.55604405e+00, -1.91374982e+01,\n",
      +       "        -1.60786921e+01,  4.31101055e+00, -1.03393089e+01,\n",
      +       "        -1.00096407e+01,  1.05612382e+01,  4.39644240e-01,\n",
      +       "         9.85617297e-01,  8.54694671e+00,  1.80330498e+00,\n",
      +       "        -2.69190844e+00, -9.81770106e-01, -8.36218204e-01,\n",
      +       "        -3.24645868e+00, -1.32388833e+01, -1.44732767e+01,\n",
      +       "         2.23467009e+01,  2.23498669e+01,  1.91215337e+01,\n",
      +       "         1.60603346e+01, -6.36846637e+00, -3.86746455e+00,\n",
      +       "        -6.66394369e+00,  4.75112518e+00, -1.75799422e+01,\n",
      +       "        -1.81218176e+01, -1.82518230e+01, -7.07802696e+00,\n",
      +       "        -7.13539082e+00, -9.35770168e+00,  5.49397086e+00,\n",
      +       "         9.29364391e+00,  9.37869873e+00,  6.98014536e+00,\n",
      +       "         6.96127606e+00]])
    • b1
      (chain, draw)
      float64
      -3.278 6.105 ... -17.81 -17.38
      array([[-3.27799514e+00,  6.10503988e+00,  6.10503988e+00,\n",
      +       "         6.41024019e-01,  6.90383879e+00,  6.95089675e+00,\n",
      +       "         8.33490774e+00,  9.37362094e+00, -1.10512973e+01,\n",
      +       "         8.70488371e-01,  3.50471653e-02,  6.81126802e+00,\n",
      +       "         7.11084258e+00,  2.39390164e+00,  1.86150864e+00,\n",
      +       "         1.74064344e+00,  1.45410781e+00,  1.13204401e+00,\n",
      +       "         8.50469590e-01,  9.41415139e-01, -6.74832229e+00,\n",
      +       "        -6.43799847e+00,  1.41269749e+00, -1.39075244e+01,\n",
      +       "        -2.06841397e+00, -2.02903497e+00, -3.85451151e+00,\n",
      +       "         9.02343120e+00, -8.70286288e+00, -1.95072046e+01,\n",
      +       "        -1.50015727e+01, -1.50549731e+01, -9.31169135e+00,\n",
      +       "        -3.86901350e+00, -3.81093157e+00, -3.80704684e+00,\n",
      +       "         1.30240557e+00, -3.40664081e+00,  3.66112380e+00,\n",
      +       "        -1.82081401e+00,  4.56746175e+00, -8.06040777e+00,\n",
      +       "         1.28964398e+01,  3.31475482e+01, -3.05639679e+01,\n",
      +       "        -6.09825497e+00, -5.37459300e+00,  6.11726321e+00,\n",
      +       "         7.40598492e+00, -8.24986189e+00, -2.04146960e+00,\n",
      +       "         6.40173236e+00,  1.30963651e+01, -1.87022542e+01,\n",
      +       "        -1.87022542e+01, -1.87622255e+01, -1.93394806e+01,\n",
      +       "        -9.85650344e+00,  1.07591202e+00,  1.17731965e+00,\n",
      +       "         1.01124817e+00, -3.77247060e+00, -2.54302489e+00,\n",
      +       "         3.06665481e+00,  8.54432312e+00,  9.23114941e+00,\n",
      +       "         5.29519574e+00,  3.07261033e+00, -1.05484761e+01,\n",
      +       "        -1.23316260e+01, -4.83124900e+00, -9.76474116e+00,\n",
      +       "        -7.21465321e+00, -6.32477531e+00, -6.29600745e+00,\n",
      +       "        -5.19948735e+00,  5.67068662e+00,  5.64918552e+00,\n",
      +       "         7.04125177e+00, -4.21700742e-01, -2.38278853e+00,\n",
      +       "        -2.88317699e+00, -4.75850575e-01, -5.93825352e+00,\n",
      +       "         2.66909953e+00, -7.02957261e-01, -6.63994189e-01,\n",
      +       "        -5.81841905e-01, -4.10721578e-01,  1.29709788e+01,\n",
      +       "         1.23991881e+01,  1.00786560e+01,  9.99168521e+00,\n",
      +       "         1.27836204e+00,  3.15990579e+00,  3.90942752e+00,\n",
      +       "         3.31087516e+00,  4.47764676e+00,  4.86988365e+00,\n",
      +       "        -5.44836604e-01],\n",
      +       "       [-9.67281405e+00,  5.17469554e-01,  5.62919615e+00,\n",
      +       "        -2.89682789e+00, -6.94707055e+00, -1.71227246e+01,\n",
      +       "        -1.65387500e+01,  1.57313760e+01,  7.23861309e+00,\n",
      +       "        -8.09482573e-01,  2.51830319e+00,  2.36147389e+00,\n",
      +       "        -5.63838046e+00, -5.46937045e+00, -3.01336756e+00,\n",
      +       "        -2.98043619e+00, -3.38447825e+00, -1.35918332e+00,\n",
      +       "         2.89682455e+00,  1.87390494e+00, -5.38601119e-01,\n",
      +       "         9.16875165e+00,  6.09162879e+00, -1.41046129e+01,\n",
      +       "         1.32579289e+01,  1.49122106e+01, -1.27382678e+01,\n",
      +       "        -1.98587676e+01,  3.08693142e+00, -8.49460029e-01,\n",
      +       "         7.17834351e-01,  1.02918588e+00, -1.03623478e+01,\n",
      +       "         3.46030786e+00,  6.05023740e+00,  1.99469398e+01,\n",
      +       "         1.90905260e+01,  3.25333053e-01,  7.08428280e+00,\n",
      +       "         7.59722363e-02, -1.72274351e+01, -1.44107936e+01,\n",
      +       "        -4.89243639e+00, -2.70897003e+00,  1.31561817e+01,\n",
      +       "        -9.82066090e+00, -4.75341842e+00,  2.87783161e+00,\n",
      +       "         4.79915778e-01,  1.89346564e+00, -6.42203524e+00,\n",
      +       "        -2.79695684e+00,  1.98904134e+00,  9.32730340e+00,\n",
      +       "         7.96387172e+00,  7.98532782e+00, -5.98252539e+00,\n",
      +       "         1.66689720e+00,  1.08111212e+01, -8.29673661e+00,\n",
      +       "         7.35987043e+00,  1.08527263e+01,  2.03155172e+01,\n",
      +       "         2.06583688e+01,  2.08578285e+01,  6.87834763e+00,\n",
      +       "         1.43973964e-01,  1.08769838e+00, -1.29250539e+01,\n",
      +       "         4.79953412e+00,  3.18760204e+00,  8.88102456e-01,\n",
      +       "        -6.90754079e+00, -2.14352253e+00, -7.99935258e+00,\n",
      +       "        -2.34722544e+00,  1.71068812e+00,  8.18835343e-01,\n",
      +       "        -9.34758177e+00,  1.04987993e+01,  3.25819648e+00,\n",
      +       "        -5.03796538e+00, -1.28900563e+01, -1.61646586e+00,\n",
      +       "        -1.17021689e+01, -5.01732319e+00, -5.01732319e+00,\n",
      +       "        -6.91179235e+00, -1.07453354e+01, -2.06873557e+00,\n",
      +       "        -2.87671281e-01,  7.21318181e+00,  2.96205376e-02,\n",
      +       "        -1.20846102e+00,  5.34092831e+00,  4.48364558e+00,\n",
      +       "         6.91106498e+00,  6.91680491e+00,  1.36446631e+01,\n",
      +       "        -1.62074732e+01],\n",
      +       "       [-1.65566924e+01,  1.59849813e+00,  5.66823141e+00,\n",
      +       "         1.75628146e+01,  4.49406368e-01,  1.34340323e+00,\n",
      +       "        -8.01374880e+00, -8.73974772e+00,  2.87683020e+00,\n",
      +       "         2.34900243e+00,  8.79801996e+00,  8.78789170e+00,\n",
      +       "         8.62284921e+00,  9.61302782e+00,  1.24955107e+01,\n",
      +       "         1.12278582e+01, -1.04933465e+01, -6.18881561e+00,\n",
      +       "        -6.19907114e+00, -5.66509248e-01, -9.44332569e-01,\n",
      +       "        -1.23107601e+01, -1.13061763e+01, -1.29832071e+01,\n",
      +       "         5.13271636e+00,  1.59251691e+01,  4.92256484e+00,\n",
      +       "        -2.13381747e+00, -2.02044437e+00,  1.15623797e+00,\n",
      +       "         2.07588574e+01, -1.82198084e+01,  1.34330868e+01,\n",
      +       "        -1.59124002e+01,  6.29703207e-02, -2.42820678e+00,\n",
      +       "        -1.80161218e+00, -1.80591873e+00, -1.92755959e+00,\n",
      +       "        -2.40054171e+00, -5.41371680e+00, -8.48225184e+00,\n",
      +       "        -1.67130609e+00,  9.77026441e-01,  8.21219619e-01,\n",
      +       "         4.56524944e-01, -1.16132162e+00, -2.95865930e+00,\n",
      +       "        -4.18896702e+00, -7.84017230e+00, -6.81906653e+00,\n",
      +       "         1.60236298e+01,  1.32872747e+01,  1.01569630e+01,\n",
      +       "        -1.48553420e+01, -8.90951198e-01, -7.10341191e+00,\n",
      +       "        -2.79067788e+00,  6.50267422e-01,  2.20696330e+01,\n",
      +       "         1.78345589e+01,  1.65134762e+01, -9.39187039e+00,\n",
      +       "        -9.58687175e+00, -2.35988247e+00, -2.30418351e+00,\n",
      +       "         2.64867160e+00, -7.01145882e+00, -7.97273458e+00,\n",
      +       "        -8.17281844e+00, -5.12643170e+00,  1.17572295e+01,\n",
      +       "        -1.73761470e+01,  3.98816017e+00, -1.19482371e+01,\n",
      +       "         1.96427055e+00,  1.97901348e+00,  3.91421388e+00,\n",
      +       "         3.79726054e+00,  8.28218258e-01,  1.47538024e+00,\n",
      +       "         6.30649408e-01,  6.24253113e-01, -8.77122616e+00,\n",
      +       "        -9.18827915e+00, -9.16158910e+00, -9.41313260e+00,\n",
      +       "         8.63048582e+00, -1.90955492e+01, -9.71928760e+00,\n",
      +       "        -9.63697781e+00, -9.08129132e+00, -6.80973228e+00,\n",
      +       "        -6.07097138e+00, -1.36592534e+00, -4.96608745e+00,\n",
      +       "        -1.45496098e+01, -1.45012536e+01, -1.35285056e+01,\n",
      +       "        -8.28739324e+00],\n",
      +       "       [ 5.75017550e+00,  1.18119239e+01,  1.59781323e+01,\n",
      +       "         1.90272781e-01, -2.25806163e+00,  1.43591274e+01,\n",
      +       "        -1.48605249e+01, -1.24360838e+01, -8.92604615e+00,\n",
      +       "        -9.03942616e+00,  5.68552136e+00, -6.20846581e+00,\n",
      +       "         6.98009503e+00,  3.68232531e+00,  2.98266851e+00,\n",
      +       "        -7.59107835e+00,  4.33251035e+00, -1.58791827e+00,\n",
      +       "        -7.91593266e+00,  5.06594563e+00,  5.06594563e+00,\n",
      +       "        -4.72218849e+00, -6.61634393e+00, -6.91117609e+00,\n",
      +       "        -8.70358627e+00,  1.58350241e+01,  1.60387155e+01,\n",
      +       "        -6.04748701e+00, -5.95640139e+00, -6.09339989e+00,\n",
      +       "         8.38998587e-02,  1.48668134e+00, -1.53683156e+01,\n",
      +       "        -2.35267477e+01, -2.48091348e+01, -2.31079355e+01,\n",
      +       "         1.93426030e+01,  1.35295223e+01,  1.57525944e+01,\n",
      +       "         1.48855862e+01,  1.48445650e+01,  1.06086757e+01,\n",
      +       "        -9.79914414e+00, -1.96843926e+00, -3.38001290e+00,\n",
      +       "        -3.21474122e+00,  9.92748222e+00,  9.80937250e+00,\n",
      +       "         8.86850136e+00,  8.74493541e+00,  8.68645799e+00,\n",
      +       "        -7.15475201e+00, -1.30509664e+00, -1.44290641e+00,\n",
      +       "         1.07046186e+01,  7.73688049e+00,  8.91093525e+00,\n",
      +       "         1.02087311e+01,  8.82389254e+00,  5.57066715e+00,\n",
      +       "         8.88524901e+00, -4.52261081e+00,  1.21624403e+01,\n",
      +       "         1.23874658e+01, -9.73215618e+00,  5.03583688e-01,\n",
      +       "         2.51794189e+00, -1.46812648e+01,  2.04822332e+00,\n",
      +       "        -2.29312914e+00,  2.17003126e+00,  4.02986723e+00,\n",
      +       "         9.51875564e+00,  1.34446256e+00, -6.08283292e-02,\n",
      +       "        -4.61656551e+00,  9.84763328e+00, -3.90479275e+00,\n",
      +       "        -3.98719629e+00,  5.02180108e+00, -1.98810079e+01,\n",
      +       "         3.01836299e+00,  2.90800505e+00,  3.48856810e+00,\n",
      +       "         7.42123761e+00,  1.16482370e+01,  8.24026449e+00,\n",
      +       "         2.38128138e+00,  1.19880306e+01, -9.19968180e+00,\n",
      +       "        -8.54797443e+00, -8.39582717e+00, -9.34283333e+00,\n",
      +       "        -9.26095226e+00, -8.79294699e+00, -1.66273106e+01,\n",
      +       "        -1.39852043e+01, -1.44124936e+01, -1.78139759e+01,\n",
      +       "        -1.73847420e+01]])
    • log_sigma
      (chain, draw)
      float64
      10.46 9.441 9.441 ... 10.61 9.831
      array([[10.45936877,  9.44145876,  9.44145876, 10.23977477, 10.32841287,\n",
      +       "        10.03617956, 10.0639785 ,  9.73055082, 10.2445188 ,  9.88425323,\n",
      +       "        10.41532777,  9.54152419, 10.11753009, 10.10656711, 10.45660446,\n",
      +       "        10.9519263 , 10.96977012,  9.55330459,  9.42759697, 10.29123281,\n",
      +       "        10.11312942, 10.56328157, 10.18631005,  9.94861132,  9.68075885,\n",
      +       "         9.91004646, 10.063593  ,  9.78886376, 10.12955968, 10.22170514,\n",
      +       "         9.68960591, 10.0589755 ,  9.87850669, 10.07703154, 10.56882854,\n",
      +       "        10.1761252 ,  9.98885584,  9.55041669, 10.09161861, 10.18120765,\n",
      +       "         9.72447255, 10.0165025 ,  9.70693474,  9.83341808,  9.94135129,\n",
      +       "         9.64486067,  9.74904101,  9.74496773,  9.57611167,  9.92040767,\n",
      +       "         9.75678911, 10.12256802,  9.4571853 ,  9.4651969 ,  9.4651969 ,\n",
      +       "        10.58311047,  9.8013769 , 10.24099228, 10.18886663,  9.80273021,\n",
      +       "        10.06257073,  9.92991328,  9.9967542 ,  9.92067661, 10.28741468,\n",
      +       "         9.80613478, 10.41245657,  9.60706214, 10.40704889, 10.43726139,\n",
      +       "         9.57608089, 10.8774256 , 10.62968812, 10.6937518 , 10.10423118,\n",
      +       "         9.48611501,  9.46213397, 10.21346749, 10.23676929, 10.18539726,\n",
      +       "         9.95084685, 10.04044368,  9.83924365,  9.84416061, 10.33560211,\n",
      +       "         9.50036865, 10.17591867, 10.74073859, 10.10646125, 10.10312756,\n",
      +       "         9.78317137,  9.98946289, 10.4452559 ,  9.46592823, 10.40692546,\n",
      +       "        10.83757011, 10.53522242, 10.09504052, 10.42206875, 10.06207938],\n",
      +       "       [10.44161794, 10.27481167,  9.48655646, 10.87538675,  9.9937803 ,\n",
      +       "         9.82199255,  9.95365017,  9.92955355,  9.69085601, 10.16530947,\n",
      +       "         9.74810315,  9.63689891, 10.12740495, 10.6588785 , 11.02641799,\n",
      +       "        10.55675814,  9.68997312, 10.18878865,  9.68414087, 10.11770556,\n",
      +       "         9.75726875,  9.9547475 ,  9.98417774,  9.96645457,  9.88036007,\n",
      +       "        10.26532839, 10.03843106,  9.85386824,  9.84126947,  9.61361351,\n",
      +       "        10.31498585, 10.49858889, 10.49736518,  9.99825041, 10.23260018,\n",
      +       "         9.90540021,  9.73163879,  9.97841598,  9.85521639, 10.43031565,\n",
      +       "        10.43522511, 10.65936095, 10.9400915 , 10.55727137,  9.62848448,\n",
      +       "         9.76376057, 10.56542682,  9.82568843,  9.87800504, 10.02528952,\n",
      +       "        10.72964825, 10.8670822 , 10.8062999 , 10.48510346, 10.85202993,\n",
      +       "        10.80686257, 10.3163652 , 10.12008471,  9.92527051,  9.71017504,\n",
      +       "         9.69119955,  9.45702444, 10.22708771, 10.55567141,  9.398097  ,\n",
      +       "         9.86198759, 10.53907268, 10.38468882, 10.54842905, 10.51516984,\n",
      +       "        10.61336484,  9.81956481, 10.03210538, 10.34453593,  9.63861686,\n",
      +       "         9.87742456, 10.0793503 , 10.26113932,  9.8563861 ,  9.87496615,\n",
      +       "         9.82091151,  9.78343076,  9.91836048, 10.0460926 , 10.26080322,\n",
      +       "         9.88325538,  9.88325538,  9.86633566, 10.03958042, 10.04208345,\n",
      +       "        10.06251192,  9.81429838, 10.19679151,  9.85940991,  9.57261832,\n",
      +       "        10.24471425, 10.01194683, 10.28484709, 10.20689838, 10.40945699],\n",
      +       "       [10.12377693,  9.60862383,  9.94369942,  9.93450784, 10.26636911,\n",
      +       "        10.31212643,  9.67506681,  9.98114075, 10.02148789, 10.04893335,\n",
      +       "        10.26977606,  9.89518261, 10.30189502, 10.27470722, 10.80163141,\n",
      +       "         9.55941176,  9.9958842 , 10.30315435, 10.05257184, 10.41826787,\n",
      +       "         9.79912147, 10.15233035, 10.1156573 , 10.07503747,  9.61940664,\n",
      +       "        10.41620371, 10.39301546, 10.51319878, 10.55494527,  9.96557033,\n",
      +       "        10.08800357, 10.15711433, 10.03677111,  9.70478165,  9.90023344,\n",
      +       "         9.91236606, 10.40573276, 10.50076185, 10.49224428, 10.06134012,\n",
      +       "        10.14199647, 10.20650718,  9.70412231, 10.06283611,  9.76493854,\n",
      +       "        10.71066398, 10.85059119, 10.61429626,  9.75422242,  9.75641018,\n",
      +       "         9.91621972,  9.70650694, 10.31953022, 10.59307556, 10.05641028,\n",
      +       "        10.12899664, 10.09535186,  9.4444989 , 10.56503302, 10.22212432,\n",
      +       "         9.77353929, 10.20705055,  9.73089987,  9.85452664,  9.73821177,\n",
      +       "        10.34359832, 10.19908808,  9.91582806,  9.75865   , 10.4944115 ,\n",
      +       "        10.35861379, 10.35203153,  9.68050287,  9.87246331, 10.41351289,\n",
      +       "         9.46705272, 10.04967185,  9.85836943,  9.67019282,  9.87178341,\n",
      +       "         9.80119854, 10.05725457,  9.79831918, 10.19040862,  9.3650871 ,\n",
      +       "        10.32650082, 10.02952907,  9.82359068, 10.00362632, 10.16258019,\n",
      +       "        10.1763594 , 10.79694928,  9.88431957,  9.943398  , 10.63034697,\n",
      +       "         9.4024417 , 10.36016358, 10.09413593,  9.63717123,  9.6011557 ],\n",
      +       "       [10.57471076,  9.83281216,  9.87464886, 10.09748377,  9.88521225,\n",
      +       "         9.96931362, 10.45859087,  9.4957097 , 10.46045724,  9.82952192,\n",
      +       "        10.20621308,  9.84384102,  9.76717385, 10.14947683,  9.74496715,\n",
      +       "        10.13230071, 10.09311964,  9.93247843, 10.54889267,  9.4921714 ,\n",
      +       "         9.4921714 ,  9.51219129, 11.10959626, 10.15116194, 10.21420786,\n",
      +       "         9.58340022, 10.26801506,  9.62964894, 10.39526836,  9.84085849,\n",
      +       "        10.25064599, 10.16850427,  9.91386995,  9.70589924,  9.5816964 ,\n",
      +       "        11.0332485 ,  9.94395884,  9.96553723, 10.05838278, 10.01240107,\n",
      +       "         9.64041223, 10.33330636, 10.38920658, 10.24981589, 10.11306576,\n",
      +       "         9.78533494, 10.14933778,  9.90840843, 10.73115648, 10.60411384,\n",
      +       "         9.82756252,  9.79568629,  9.44653392,  9.69505924,  9.908923  ,\n",
      +       "        10.25532307, 10.33979149,  9.72010603,  9.79529067,  9.64296301,\n",
      +       "         9.87248565,  9.88646605,  9.86473177, 10.43373282, 10.51827521,\n",
      +       "         9.59840316, 10.61359029, 10.06970044,  9.90349604, 10.23505053,\n",
      +       "         9.74536039,  9.98515559,  9.82643717, 10.5196737 , 10.32713049,\n",
      +       "        10.55228372, 10.42044207,  9.92562612, 10.19430325, 10.27656402,\n",
      +       "        10.12377467, 10.27575575,  9.5810486 ,  9.83277969,  9.99873766,\n",
      +       "         9.98182429,  9.86797744,  9.88180466, 10.37230909,  9.74651764,\n",
      +       "        10.37910871,  9.97110924,  9.91102333, 10.22787875,  9.77934209,\n",
      +       "        10.16016515, 10.21202814,  9.95238626, 10.60890935,  9.83121668]])
    • sigma
      (chain, draw)
      float64
      3.487e+04 1.26e+04 ... 1.861e+04
      array([[34869.53389097, 12600.0839793 , 12600.0839793 , 27994.82000183,\n",
      +       "        30589.52391146, 22837.9649113 , 23481.74299687, 16823.816723  ,\n",
      +       "        28127.94379918, 19618.98960375, 33367.17024214, 13926.1576343 ,\n",
      +       "        24773.50689664, 24503.39863131, 34773.27659229, 57063.86142756,\n",
      +       "        58091.23766844, 14091.18344631, 12426.6292162 , 29473.08670032,\n",
      +       "        24664.72626426, 38687.87698917, 26537.39236547, 20923.14664794,\n",
      +       "        16006.63901104, 20131.60933566, 23472.69251956, 17834.03084086,\n",
      +       "        25073.32172228, 27493.50672461, 16148.87885547, 23364.55721214,\n",
      +       "        19506.57163715, 23790.26020766, 38903.07356466, 26268.48474359,\n",
      +       "        21782.36195695, 14050.54820281, 24139.83388786, 26402.33285677,\n",
      +       "        16721.86709017, 22392.97327053, 16431.15889456, 18646.5808638 ,\n",
      +       "        20771.79405968, 15442.22115857, 17137.78590548, 17068.12087712,\n",
      +       "        14416.25505773, 20341.28146493, 17271.08692711, 24898.62899437,\n",
      +       "        12799.80607327, 12902.76494545, 12902.76494545, 39462.67108797,\n",
      +       "        18058.59272917, 28028.92460813, 26605.32415603, 18083.04812757,\n",
      +       "        23448.70917993, 20535.55968208, 21955.08820415, 20346.75278927,\n",
      +       "        29360.76926473, 18144.71811935, 33271.50387733, 14869.42160265,\n",
      +       "        33092.06773658, 34107.11834374, 14415.81128636, 52967.06576072,\n",
      +       "        41344.2288585 , 44079.5751207 , 24446.22717377, 13175.50907376,\n",
      +       "        12863.3050945 , 27267.95520941, 27910.80851014, 26513.18047842,\n",
      +       "        20969.97334878, 22935.55670564, 18755.52492838, 18847.97217157,\n",
      +       "        30810.2317305 , 13364.65280786, 26263.06001516, 46200.16227381,\n",
      +       "        24500.80481863, 24419.26290344, 17732.80111842, 21795.5889185 ,\n",
      +       "        34380.88071261, 12912.20454105, 33087.98365216, 50897.55230572,\n",
      +       "        37617.41625576, 24222.57974862, 33592.85764411, 23437.19049347],\n",
      +       "       [34256.03191017, 28993.0571633 , 13181.32669381, 52859.18417331,\n",
      +       "        21889.89302989, 18434.74640156, 21028.84138346, 20528.17363023,\n",
      +       "        16169.07924917, 25985.90271729, 17121.72058651, 15319.76198536,\n",
      +       "        25019.35374728, 42568.86928963, 61476.97461318, 38436.32045791,\n",
      +       "        16154.81004444, 26603.24944546, 16060.86534309, 24777.8543516 ,\n",
      +       "        17279.37284323, 21051.9294992 , 21680.69984389, 21299.83434104,\n",
      +       "        19542.75823093, 28719.40753725, 22889.44248294, 19031.83220365,\n",
      +       "        18793.55870062, 14967.1564282 , 30181.54283375, 36264.29365569,\n",
      +       "        36219.94377792, 21987.96227698, 27794.68749521, 20038.28977411,\n",
      +       "        16842.13043047, 21556.14011034, 19057.50742454, 33871.0399469 ,\n",
      +       "        34037.73717794, 42589.41190998, 56392.50281441, 38456.05232953,\n",
      +       "        15191.39584423, 17391.91228341, 38770.9610398 , 18503.00501521,\n",
      +       "        19496.78860166, 22590.60786318, 45690.61747878, 52422.02970011,\n",
      +       "        49330.60195757, 35778.5367523 , 51638.86819276, 49358.36660372,\n",
      +       "        30223.2023924 , 24836.87464619, 20440.43874056, 16484.48709978,\n",
      +       "        16174.6349876 , 12797.74729169, 27641.89166264, 38394.57339327,\n",
      +       "        12065.39845644, 19186.98738818, 37762.53213102, 32360.33816013,\n",
      +       "        38117.51067222, 36870.60263071, 40674.833659  , 18390.04580594,\n",
      +       "        22745.10820345, 31086.71801519, 15346.10325645, 19485.47435308,\n",
      +       "        23845.48812466, 28599.35132191, 19079.81221957, 19437.62978066,\n",
      +       "        18414.82837664, 17737.40127752, 20299.68168244, 23065.4845344 ,\n",
      +       "        28589.74075383, 19599.4224973 , 19599.4224973 , 19270.59535838,\n",
      +       "        22915.76587179, 22973.19656761, 23447.33026792, 18293.45045331,\n",
      +       "        26817.00582319, 19137.5932564 , 14365.98186107, 28133.44198899,\n",
      +       "        22291.19029722, 29285.47946237, 27089.41621347, 33171.85271644],\n",
      +       "       [24928.74737221, 14892.66117205, 20820.62625865, 20630.12863282,\n",
      +       "        28749.31174005, 30095.36432049, 15915.78731594, 21614.95568982,\n",
      +       "        22504.88984273, 23131.10086572, 28847.4264676 , 19834.58895372,\n",
      +       "        29789.01629224, 28990.02887173, 49100.83941758, 14177.50390657,\n",
      +       "        21935.99555024, 29826.55388245, 23215.41657408, 33465.4175907 ,\n",
      +       "        18017.90878008, 25650.80803587, 24727.15478921, 23742.86798702,\n",
      +       "        15054.11482482, 33396.41065728, 32630.91607615, 36798.00011307,\n",
      +       "        38366.7037266 , 21281.00832435, 24052.72496058, 25773.81488022,\n",
      +       "        22851.4788394 , 16395.81917241, 19935.02348599, 20178.36076356,\n",
      +       "        33048.54299033, 36343.18035373, 36034.93908428, 23419.87083197,\n",
      +       "        25387.10056666, 27078.82063953, 16385.01231691, 23454.93280462,\n",
      +       "        17412.41158915, 44831.39625974, 51564.62695884, 40712.73666325,\n",
      +       "        17226.81425184, 17264.54373334, 20256.27142207, 16424.13115491,\n",
      +       "        30319.01090096, 39857.88609969, 23304.69874493, 25059.20831953,\n",
      +       "        24230.12225648, 12638.44836329, 38755.69623779, 27505.03408825,\n",
      +       "        17562.81721622, 27093.53865581, 16829.6900193 , 19044.367001  ,\n",
      +       "        16953.19799027, 31057.58422942, 26878.66368055, 20248.33925648,\n",
      +       "        17303.25657652, 36113.11959108, 31527.44738997, 31320.60696758,\n",
      +       "        16002.5421142 , 19389.04132618, 33306.66769125, 12926.73229189,\n",
      +       "        23148.18943094, 19117.69129382, 15838.40269797, 19375.86331156,\n",
      +       "        18055.37202265, 23324.38284396, 18003.45885819, 26646.38099544,\n",
      +       "        11673.62262632, 30531.0910574 , 22686.58531689, 18464.23102824,\n",
      +       "        22106.48581242, 25915.07662758, 26274.6374334 , 48871.48019513,\n",
      +       "        19620.2910538 , 20814.35150461, 41371.47744477, 12117.93294682,\n",
      +       "        31576.3461099 , 24200.67803387, 15323.93442524, 14781.85510155],\n",
      +       "       [39132.5843376 , 18635.28597428, 19431.46342635, 24281.83374877,\n",
      +       "        19637.81357746, 21360.81860576, 34842.41948033, 13302.53232004,\n",
      +       "        34907.50893506, 18574.07212888, 27070.85798435, 18841.94951253,\n",
      +       "        17451.37718858, 25577.71709907, 17068.11107692, 25142.14261273,\n",
      +       "        24176.09558099, 20588.30401745, 38135.18678888, 13255.54717536,\n",
      +       "        13255.54717536, 13523.59605048, 66809.2123045 , 25620.85485895,\n",
      +       "        27288.15109968, 14521.71250918, 28796.67069798, 15209.09582211,\n",
      +       "        32704.51306008, 18785.83646348, 28300.81814788, 26069.05519289,\n",
      +       "        20208.72953035, 16414.15325127, 14496.99115223, 61898.33148158,\n",
      +       "        20826.02820653, 21280.30396979, 23350.71257724, 22301.31824124,\n",
      +       "        15373.67987275, 30739.5800401 , 32506.86505141, 28277.33542856,\n",
      +       "        24663.1563225 , 17771.20881001, 25574.16078737, 20098.66006723,\n",
      +       "        45759.58146402, 40300.28574261, 18537.71372806, 17956.12008676,\n",
      +       "        12664.19400878, 16237.18458027, 20109.00500846, 28433.49337087,\n",
      +       "        30939.57831256, 16649.00991175, 17949.01767671, 15412.94488422,\n",
      +       "        19389.4746632 , 19662.45098429, 19239.7123638 , 33986.98088334,\n",
      +       "        36985.2774309 , 14741.22334744, 40684.00490071, 23616.48919825,\n",
      +       "        20000.16980899, 27862.87747076, 17074.82423249, 21701.91076628,\n",
      +       "        18516.86404169, 37037.03748927, 30550.32143428, 38264.72445841,\n",
      +       "        33538.25712661, 20447.70887902, 26750.36104043, 29043.90752422,\n",
      +       "        24928.69097115, 29020.44178522, 14487.60307767, 18634.6809147 ,\n",
      +       "        21998.67854328, 21629.73542355, 19302.25944826, 19571.00984293,\n",
      +       "        31962.19532739, 17094.59558593, 32180.26666895, 21399.20894472,\n",
      +       "        20151.28483907, 27663.76599205, 17665.02708076, 25852.56635078,\n",
      +       "        27228.73544964, 21002.27958156, 40494.01027687, 18605.57742447]])
  • created_at :
    2019-11-10T20:53:29.353030
    inference_library :
    pystan
    inference_library_version :
    2.19.1.1
" + ], + "text/plain": [ + "\n", + "Dimensions: (chain: 4, draw: 100)\n", + "Coordinates:\n", + " * chain (chain) int64 0 1 2 3\n", + " * draw (draw) int64 0 1 2 3 4 5 6 7 8 9 ... 91 92 93 94 95 96 97 98 99\n", + "Data variables:\n", + " b0 (chain, draw) float64 12.18 -0.1928 -0.1928 ... 9.379 6.98 6.961\n", + " b1 (chain, draw) float64 -3.278 6.105 6.105 ... -14.41 -17.81 -17.38\n", + " log_sigma (chain, draw) float64 10.46 9.441 9.441 ... 9.952 10.61 9.831\n", + " sigma (chain, draw) float64 3.487e+04 1.26e+04 ... 4.049e+04 1.861e+04\n", + "Attributes:\n", + " created_at: 2019-11-10T20:53:29.353030\n", + " inference_library: pystan\n", + " inference_library_version: 2.19.1.1" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "idata_stan.posterior" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + "\n", + "\n", + "Show/Hide data repr\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "Show/Hide attributes\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "
xarray.Dataset
    • chain: 4
    • developer: 5
    • draw: 100
    • chain
      (chain)
      int64
      0 1 2 3
      array([0, 1, 2, 3])
    • draw
      (draw)
      int64
      0 1 2 3 4 5 6 ... 94 95 96 97 98 99
      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,\n",
      +       "       18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,\n",
      +       "       36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53,\n",
      +       "       54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71,\n",
      +       "       72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89,\n",
      +       "       90, 91, 92, 93, 94, 95, 96, 97, 98, 99])
    • developer
      (developer)
      object
      'Alice' 'Bob' ... 'Erika'
      array(['Alice', 'Bob', 'Cole', 'Danielle', 'Erika'], dtype=object)
    • accept_stat
      (chain, draw)
      float64
      0.8935 0.9752 ... 0.4978 0.9424
      array([[0.89354042, 0.97522053, 0.67382396, 0.78312029, 0.9834467 ,\n",
      +       "        0.74909871, 0.99746658, 0.98929514, 0.96283086, 0.98390158,\n",
      +       "        0.89588415, 0.98776334, 0.95329117, 0.99884204, 0.91057932,\n",
      +       "        0.47344384, 0.78674663, 0.36261285, 0.53588548, 0.52266599,\n",
      +       "        0.98073435, 0.82335135, 0.92255228, 0.94630666, 0.95623623,\n",
      +       "        1.        , 0.98485841, 0.998511  , 0.96474799, 0.98581776,\n",
      +       "        0.99773155, 0.95100895, 0.99952738, 0.99008275, 0.85863202,\n",
      +       "        0.91386526, 0.99137902, 0.91329611, 0.98996235, 0.95340993,\n",
      +       "        0.99767911, 0.99871036, 0.97515452, 0.96208442, 0.9402117 ,\n",
      +       "        0.93077538, 0.99977605, 0.95771316, 0.88626491, 0.9874038 ,\n",
      +       "        0.97864994, 0.99713844, 0.87921366, 0.78510321, 0.27838452,\n",
      +       "        1.        , 0.9854227 , 0.94047739, 0.98868791, 0.97037771,\n",
      +       "        0.99989718, 0.9637383 , 0.92310865, 0.96175223, 0.93311045,\n",
      +       "        0.94708603, 0.88437197, 0.93600895, 0.97768594, 0.97597884,\n",
      +       "        0.97614664, 0.56413286, 0.92569613, 0.90765361, 1.        ,\n",
      +       "        0.85359079, 0.99031437, 0.74871064, 0.99234743, 0.99153272,\n",
      +       "        0.99685073, 0.99300731, 0.97108304, 0.93929612, 0.92928464,\n",
      +       "        0.96951136, 0.99982681, 0.92346545, 1.        , 0.99871063,\n",
      +       "        0.99904412, 1.        , 0.84479301, 0.93669198, 1.        ,\n",
      +       "        0.63326839, 0.85216722, 0.40037312, 0.89421408, 0.98054367],\n",
      +       "       [0.90037253, 0.99667095, 0.35498887, 0.62154133, 0.9740158 ,\n",
      +       "        0.95588104, 0.99998429, 0.99409555, 0.95922516, 0.99709708,\n",
      +       "        0.99518853, 0.82380516, 0.98336825, 0.88381222, 0.95573132,\n",
      +       "        1.        , 0.98627344, 0.99832317, 0.98338524, 0.9115459 ,\n",
      +       "        0.96621541, 0.99536503, 0.99803177, 0.93899002, 0.99935938,\n",
      +       "        0.94749812, 0.98435338, 0.98242895, 0.99999461, 0.93983696,\n",
      +       "        1.        , 0.94248546, 0.98248345, 0.97621438, 0.96348963,\n",
      +       "        0.96742324, 0.96641668, 0.92049842, 0.99841078, 0.90242413,\n",
      +       "        0.99253355, 0.9623285 , 0.92529777, 0.98155041, 0.98388149,\n",
      +       "        0.99961244, 0.79659458, 0.97896067, 0.95315486, 0.99625163,\n",
      +       "        0.83256242, 0.84989297, 0.97258511, 0.96910162, 0.93722322,\n",
      +       "        1.        , 0.98369397, 0.95317654, 0.99929084, 0.96203748,\n",
      +       "        0.99937745, 0.83648462, 0.96133885, 0.95761096, 0.96341766,\n",
      +       "        0.97458855, 0.82427008, 0.88166513, 0.97002408, 0.98796582,\n",
      +       "        0.94742315, 0.97116889, 0.99942439, 0.95768741, 0.99667618,\n",
      +       "        0.99933616, 0.95700986, 0.96947967, 0.98733582, 0.99592585,\n",
      +       "        0.96303103, 0.99641959, 0.99825692, 0.83151393, 0.97941115,\n",
      +       "        0.99810964, 0.59704247, 0.83475223, 0.99819602, 0.99071434,\n",
      +       "        0.99912974, 0.999131  , 0.9379846 , 0.98691434, 0.93684059,\n",
      +       "        0.99999225, 0.98552408, 0.96777396, 0.98980976, 0.98341885],\n",
      +       "       [0.9805512 , 0.97200821, 0.99597153, 0.95788563, 0.93423837,\n",
      +       "        0.98528744, 0.97791487, 0.98606412, 0.99565226, 0.99863805,\n",
      +       "        0.93527806, 0.97230715, 0.88843231, 0.97809905, 0.44548777,\n",
      +       "        0.99117556, 0.99772184, 0.87396327, 0.97499904, 0.93687812,\n",
      +       "        0.98825137, 0.98366017, 0.99774385, 0.99952729, 0.96066358,\n",
      +       "        0.96722572, 0.99042366, 0.97655339, 0.9847378 , 0.93224689,\n",
      +       "        0.98772216, 0.99489306, 0.99931537, 0.89585808, 0.99772339,\n",
      +       "        0.99983723, 0.89180882, 0.97875605, 0.98420216, 0.95718918,\n",
      +       "        0.99288958, 0.97898635, 0.99058665, 0.99451424, 0.9874268 ,\n",
      +       "        0.77770789, 0.89099848, 0.95665826, 0.92477077, 0.80929793,\n",
      +       "        0.99032882, 0.9751292 , 0.92018918, 0.97149299, 0.92507819,\n",
      +       "        0.99365398, 0.99359871, 0.8871786 , 0.89470371, 0.97976491,\n",
      +       "        0.9982615 , 0.97243308, 0.96057645, 0.9999028 , 0.86664467,\n",
      +       "        0.84718588, 0.99415635, 0.99720842, 0.98158141, 0.37862812,\n",
      +       "        0.9897682 , 0.97102644, 0.9925586 , 0.99309043, 0.8692112 ,\n",
      +       "        0.97034125, 0.91663155, 0.99847057, 0.69997357, 0.99939059,\n",
      +       "        0.9862938 , 0.99942876, 0.97433119, 0.93536616, 0.60087344,\n",
      +       "        0.27671317, 0.99338884, 0.99948663, 0.99997117, 0.98437406,\n",
      +       "        0.99052647, 0.82608042, 0.60271819, 0.92272285, 0.86095909,\n",
      +       "        0.92582835, 0.4666995 , 0.99541163, 0.92642186, 0.99560812],\n",
      +       "       [0.95802642, 0.98303635, 0.97816226, 0.95916344, 0.97570654,\n",
      +       "        0.99229428, 0.91746484, 0.97989274, 0.99952203, 0.81217512,\n",
      +       "        0.96168849, 0.98770662, 0.98946422, 0.9940034 , 0.99906682,\n",
      +       "        0.99684139, 0.99655712, 0.91196627, 0.65956471, 0.83877653,\n",
      +       "        0.62001433, 0.99242631, 0.2707486 , 1.        , 0.98883229,\n",
      +       "        0.98266331, 0.99830427, 0.98530549, 0.92100993, 0.98483894,\n",
      +       "        0.9526326 , 0.98821132, 0.97922113, 0.93230101, 0.93066528,\n",
      +       "        0.38541567, 0.97307057, 0.92637501, 0.98235691, 0.99899392,\n",
      +       "        0.96426336, 0.62645681, 0.98306828, 0.98218535, 0.99712426,\n",
      +       "        0.97613233, 0.93301283, 0.98708239, 0.45406578, 1.        ,\n",
      +       "        0.89873849, 0.99572819, 0.65961647, 1.        , 0.99976997,\n",
      +       "        0.90425571, 0.98939943, 0.99340127, 0.99466852, 0.95102405,\n",
      +       "        0.99390147, 0.98204169, 0.97888889, 0.62480659, 0.97085936,\n",
      +       "        0.94520561, 0.64684731, 0.93031785, 0.99766647, 0.90992961,\n",
      +       "        0.99730027, 0.98391857, 0.99681528, 0.84760748, 0.98936996,\n",
      +       "        0.9499367 , 0.98463622, 0.9926395 , 0.90663506, 0.97599595,\n",
      +       "        0.99381726, 0.97843988, 0.67677688, 0.99657568, 0.98333476,\n",
      +       "        0.99337245, 0.92501667, 0.99960547, 0.90490473, 0.6159008 ,\n",
      +       "        0.54143695, 0.99213943, 0.99833448, 0.91190088, 0.75572537,\n",
      +       "        0.60105959, 0.99406572, 1.        , 0.49784409, 0.94241233]])
    • stepsize
      (chain, draw)
      float64
      0.3148 0.3148 ... 0.2926 0.2926
      array([[0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 ,\n",
      +       "        0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 ,\n",
      +       "        0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 ,\n",
      +       "        0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 ,\n",
      +       "        0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 ,\n",
      +       "        0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 ,\n",
      +       "        0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 ,\n",
      +       "        0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 ,\n",
      +       "        0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 ,\n",
      +       "        0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 ,\n",
      +       "        0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 ,\n",
      +       "        0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 ,\n",
      +       "        0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 ,\n",
      +       "        0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 ,\n",
      +       "        0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 ,\n",
      +       "        0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 ,\n",
      +       "        0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 ,\n",
      +       "        0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 ,\n",
      +       "        0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 ,\n",
      +       "        0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 , 0.3148291 ],\n",
      +       "       [0.24964835, 0.24964835, 0.24964835, 0.24964835, 0.24964835,\n",
      +       "        0.24964835, 0.24964835, 0.24964835, 0.24964835, 0.24964835,\n",
      +       "        0.24964835, 0.24964835, 0.24964835, 0.24964835, 0.24964835,\n",
      +       "        0.24964835, 0.24964835, 0.24964835, 0.24964835, 0.24964835,\n",
      +       "        0.24964835, 0.24964835, 0.24964835, 0.24964835, 0.24964835,\n",
      +       "        0.24964835, 0.24964835, 0.24964835, 0.24964835, 0.24964835,\n",
      +       "        0.24964835, 0.24964835, 0.24964835, 0.24964835, 0.24964835,\n",
      +       "        0.24964835, 0.24964835, 0.24964835, 0.24964835, 0.24964835,\n",
      +       "        0.24964835, 0.24964835, 0.24964835, 0.24964835, 0.24964835,\n",
      +       "        0.24964835, 0.24964835, 0.24964835, 0.24964835, 0.24964835,\n",
      +       "        0.24964835, 0.24964835, 0.24964835, 0.24964835, 0.24964835,\n",
      +       "        0.24964835, 0.24964835, 0.24964835, 0.24964835, 0.24964835,\n",
      +       "        0.24964835, 0.24964835, 0.24964835, 0.24964835, 0.24964835,\n",
      +       "        0.24964835, 0.24964835, 0.24964835, 0.24964835, 0.24964835,\n",
      +       "        0.24964835, 0.24964835, 0.24964835, 0.24964835, 0.24964835,\n",
      +       "        0.24964835, 0.24964835, 0.24964835, 0.24964835, 0.24964835,\n",
      +       "        0.24964835, 0.24964835, 0.24964835, 0.24964835, 0.24964835,\n",
      +       "        0.24964835, 0.24964835, 0.24964835, 0.24964835, 0.24964835,\n",
      +       "        0.24964835, 0.24964835, 0.24964835, 0.24964835, 0.24964835,\n",
      +       "        0.24964835, 0.24964835, 0.24964835, 0.24964835, 0.24964835],\n",
      +       "       [0.27024578, 0.27024578, 0.27024578, 0.27024578, 0.27024578,\n",
      +       "        0.27024578, 0.27024578, 0.27024578, 0.27024578, 0.27024578,\n",
      +       "        0.27024578, 0.27024578, 0.27024578, 0.27024578, 0.27024578,\n",
      +       "        0.27024578, 0.27024578, 0.27024578, 0.27024578, 0.27024578,\n",
      +       "        0.27024578, 0.27024578, 0.27024578, 0.27024578, 0.27024578,\n",
      +       "        0.27024578, 0.27024578, 0.27024578, 0.27024578, 0.27024578,\n",
      +       "        0.27024578, 0.27024578, 0.27024578, 0.27024578, 0.27024578,\n",
      +       "        0.27024578, 0.27024578, 0.27024578, 0.27024578, 0.27024578,\n",
      +       "        0.27024578, 0.27024578, 0.27024578, 0.27024578, 0.27024578,\n",
      +       "        0.27024578, 0.27024578, 0.27024578, 0.27024578, 0.27024578,\n",
      +       "        0.27024578, 0.27024578, 0.27024578, 0.27024578, 0.27024578,\n",
      +       "        0.27024578, 0.27024578, 0.27024578, 0.27024578, 0.27024578,\n",
      +       "        0.27024578, 0.27024578, 0.27024578, 0.27024578, 0.27024578,\n",
      +       "        0.27024578, 0.27024578, 0.27024578, 0.27024578, 0.27024578,\n",
      +       "        0.27024578, 0.27024578, 0.27024578, 0.27024578, 0.27024578,\n",
      +       "        0.27024578, 0.27024578, 0.27024578, 0.27024578, 0.27024578,\n",
      +       "        0.27024578, 0.27024578, 0.27024578, 0.27024578, 0.27024578,\n",
      +       "        0.27024578, 0.27024578, 0.27024578, 0.27024578, 0.27024578,\n",
      +       "        0.27024578, 0.27024578, 0.27024578, 0.27024578, 0.27024578,\n",
      +       "        0.27024578, 0.27024578, 0.27024578, 0.27024578, 0.27024578],\n",
      +       "       [0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 ,\n",
      +       "        0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 ,\n",
      +       "        0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 ,\n",
      +       "        0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 ,\n",
      +       "        0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 ,\n",
      +       "        0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 ,\n",
      +       "        0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 ,\n",
      +       "        0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 ,\n",
      +       "        0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 ,\n",
      +       "        0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 ,\n",
      +       "        0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 ,\n",
      +       "        0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 ,\n",
      +       "        0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 ,\n",
      +       "        0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 ,\n",
      +       "        0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 ,\n",
      +       "        0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 ,\n",
      +       "        0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 ,\n",
      +       "        0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 ,\n",
      +       "        0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 ,\n",
      +       "        0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 , 0.2925687 ]])
    • treedepth
      (chain, draw)
      int64
      6 6 1 5 5 2 7 7 ... 6 2 5 6 6 3 6 3
      array([[6, 6, 1, 5, 5, 2, 7, 7, 7, 6, 5, 5, 2, 5, 5, 5, 2, 3, 2, 2, 5, 2,\n",
      +       "        6, 6, 6, 2, 7, 6, 7, 5, 5, 2, 6, 7, 2, 3, 6, 6, 7, 6, 7, 6, 7, 6,\n",
      +       "        7, 6, 6, 6, 5, 7, 5, 7, 6, 7, 2, 3, 3, 7, 5, 2, 4, 5, 5, 5, 5, 6,\n",
      +       "        6, 6, 7, 5, 7, 6, 4, 4, 2, 4, 7, 3, 5, 6, 6, 5, 6, 6, 7, 5, 2, 1,\n",
      +       "        2, 6, 3, 6, 1, 7, 4, 2, 3, 4, 3, 6],\n",
      +       "       [7, 6, 5, 6, 6, 6, 7, 7, 7, 6, 6, 2, 6, 2, 5, 2, 5, 5, 6, 5, 6, 6,\n",
      +       "        7, 7, 7, 6, 6, 6, 7, 6, 5, 5, 7, 7, 7, 7, 6, 6, 7, 7, 7, 4, 7, 4,\n",
      +       "        7, 7, 6, 6, 6, 5, 7, 5, 5, 6, 4, 1, 7, 7, 7, 7, 7, 6, 5, 3, 4, 6,\n",
      +       "        6, 3, 6, 6, 4, 6, 6, 7, 6, 6, 6, 5, 6, 7, 6, 7, 7, 7, 7, 7, 1, 4,\n",
      +       "        6, 7, 6, 7, 7, 6, 7, 6, 5, 2, 7, 7],\n",
      +       "       [7, 7, 6, 7, 7, 4, 6, 3, 7, 5, 7, 1, 4, 4, 5, 3, 7, 6, 1, 6, 3, 6,\n",
      +       "        6, 4, 7, 6, 6, 6, 5, 5, 6, 7, 7, 7, 6, 6, 3, 6, 3, 4, 5, 7, 6, 5,\n",
      +       "        3, 2, 4, 6, 4, 5, 4, 7, 4, 6, 7, 6, 7, 5, 6, 7, 5, 6, 6, 6, 7, 3,\n",
      +       "        6, 6, 4, 3, 4, 7, 7, 7, 7, 6, 2, 6, 2, 7, 6, 6, 1, 7, 3, 2, 3, 6,\n",
      +       "        6, 6, 4, 5, 5, 6, 5, 5, 5, 2, 7, 7],\n",
      +       "       [6, 5, 6, 7, 5, 7, 7, 6, 7, 2, 7, 7, 6, 6, 6, 6, 7, 6, 6, 6, 1, 5,\n",
      +       "        3, 2, 4, 7, 2, 6, 2, 3, 6, 4, 7, 5, 7, 4, 6, 5, 5, 4, 2, 5, 7, 7,\n",
      +       "        6, 2, 5, 2, 2, 2, 4, 7, 6, 2, 7, 5, 4, 4, 4, 6, 5, 6, 6, 5, 6, 6,\n",
      +       "        4, 7, 7, 7, 7, 6, 5, 6, 5, 5, 6, 6, 5, 6, 7, 7, 2, 4, 6, 7, 5, 7,\n",
      +       "        7, 7, 6, 2, 6, 2, 5, 6, 6, 3, 6, 3]])
    • n_leapfrog
      (chain, draw)
      int64
      79 87 3 43 63 3 ... 127 63 9 123 11
      array([[ 79,  87,   3,  43,  63,   3, 127, 127, 127,  79,  39,  59,   3,\n",
      +       "         63,  51,  49,   5,  11,   3,   3,  55,   7,  71, 127, 127,   3,\n",
      +       "        127,  95, 127,  35,  63,   3,  63, 127,   3,  11,  83,  87, 127,\n",
      +       "         83, 127,  67, 127,  95, 127,  63, 127,  75,  39, 127,  43, 127,\n",
      +       "         63, 127,   3,  11,  15, 127,  59,   3,  19,  51,  43,  55,  39,\n",
      +       "        127, 127,  67, 127,  35, 127, 127,  19,  31,   3,  31, 127,  15,\n",
      +       "         39,  63,  63,  31,  63,  63, 127,  47,   7,   3,   3,  71,  15,\n",
      +       "         63,   3, 127,  31,   7,  11,  31,  15,  63],\n",
      +       "       [127, 103,  51,  79,  79,  95, 127, 127, 127, 127,  95,   3,  75,\n",
      +       "          3,  39,   3,  47,  63,  95,  51,  95, 127, 127, 127, 127,  63,\n",
      +       "        127, 119, 127,  63,  51,  47, 127, 127, 127, 127,  63,  95, 127,\n",
      +       "        127, 127,  23, 127,  23, 127, 127, 127,  67,  63,  31, 127,  39,\n",
      +       "         55, 111,  27,   1, 127, 127, 127, 127, 127,  71,  55,  11,  19,\n",
      +       "        103,  83,  15,  71,  77,  19,  87, 127, 127, 127,  75, 107,  35,\n",
      +       "        107, 127, 127, 127, 127, 127, 127, 127,   3,  19, 127, 127, 111,\n",
      +       "        127, 127,  95, 127,  75,  63,   3, 127, 127],\n",
      +       "       [127, 127,  63, 127, 127,  31, 127,  15, 127,  63, 127,   3,  19,\n",
      +       "         31,  51,  11, 127, 127,   3,  95,  15, 127,  63,  31, 127,  63,\n",
      +       "        127, 127,  51,  59,  63, 127, 127, 127, 127,  95,  11,  67,  15,\n",
      +       "         23,  59, 127,  91,  59,  11,   7,  27,  75,  19,  39,  19, 127,\n",
      +       "         27, 127, 127, 127, 127,  43,  67, 127,  31,  63, 127, 127, 127,\n",
      +       "         15,  67, 127,  31,  15,  31, 127, 127, 127, 127,  71,   3,  95,\n",
      +       "          3, 127, 127,  79,   3, 127,  15,   3,  15, 127, 127,  63,  19,\n",
      +       "         35,  39,  67,  43,  43,  55,   7, 127, 127],\n",
      +       "       [ 71,  39,  63, 127,  63, 127, 127, 127, 127,   3, 127, 127,  75,\n",
      +       "        127,  95,  63, 127,  71, 111,  83,   1,  55,  11,   3,  31, 127,\n",
      +       "          7, 127,   3,  15,  63,  23, 127,  63, 127,  23,  87,  47,  39,\n",
      +       "         19,   3,  35, 127, 127,  63,   3,  63,   7,   3,   3,  31, 127,\n",
      +       "         63,   3, 127,  39,  23,  19,  31,  63,  59,  87, 127,  35,  75,\n",
      +       "        127,  23, 127, 127, 127, 127, 127,  55, 127,  47,  63,  71,  71,\n",
      +       "         47, 127, 127, 127,   3,  23,  63, 127,  51, 127, 127, 127,  63,\n",
      +       "          7,  63,   7,  51, 127,  63,   9, 123,  11]])
    • diverging
      (chain, draw)
      bool
      False False False ... False False
      array([[False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False],\n",
      +       "       [False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False],\n",
      +       "       [False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False],\n",
      +       "       [False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False, False, False, False, False, False, False, False, False,\n",
      +       "        False]])
    • energy
      (chain, draw)
      float64
      55.57 55.7 54.71 ... 56.23 55.53
      array([[55.56648389, 55.69525735, 54.70830093, 55.6496889 , 53.65690962,\n",
      +       "        54.3965749 , 53.28676352, 53.92245537, 53.71872906, 53.7493869 ,\n",
      +       "        53.54177694, 55.4702215 , 54.25140099, 53.23412331, 53.5940455 ,\n",
      +       "        58.05574681, 57.72435669, 55.380867  , 54.86368086, 55.48053178,\n",
      +       "        54.63049848, 54.00442829, 54.47538013, 55.4055671 , 55.69997863,\n",
      +       "        52.79392238, 52.75398776, 53.47251534, 53.57519826, 54.60871284,\n",
      +       "        55.63996734, 53.9855171 , 53.5617845 , 53.79726852, 54.25647715,\n",
      +       "        54.37695384, 53.72493253, 54.03187046, 53.50313067, 53.62146533,\n",
      +       "        52.74149727, 53.08504846, 54.02776796, 59.55097885, 59.17373971,\n",
      +       "        58.16015866, 54.28978574, 53.36053153, 55.44651645, 55.91715651,\n",
      +       "        53.72024579, 52.79251343, 55.56306607, 58.95540081, 58.20663595,\n",
      +       "        56.49685751, 56.0476738 , 56.76746538, 56.09898948, 52.86538377,\n",
      +       "        52.33914347, 52.96070796, 53.06124005, 53.29476542, 55.88341929,\n",
      +       "        56.81440803, 55.93384513, 55.37078471, 54.26314879, 54.29882251,\n",
      +       "        54.31865513, 56.44752987, 56.42912894, 56.41161133, 54.35453024,\n",
      +       "        54.84059481, 54.33802149, 55.10497298, 53.35641317, 54.80906832,\n",
      +       "        55.67187207, 53.24429645, 53.62971246, 54.1830852 , 53.51839715,\n",
      +       "        54.76989357, 53.45519098, 54.93598152, 54.10596634, 54.01543119,\n",
      +       "        53.469745  , 53.30814796, 54.41750152, 55.13888729, 54.5793949 ,\n",
      +       "        56.01573783, 57.22654437, 59.40960802, 54.16371603, 56.18206817],\n",
      +       "       [56.19836741, 55.48173864, 57.80025125, 57.30496261, 56.23248504,\n",
      +       "        54.65053434, 54.56503764, 53.9666969 , 54.55509245, 53.36722148,\n",
      +       "        54.60836804, 53.89298816, 53.61873507, 54.50996846, 56.84096995,\n",
      +       "        55.53956782, 54.04520462, 52.73972232, 53.46642326, 53.50041764,\n",
      +       "        53.62974507, 53.4999606 , 52.8315695 , 56.24735357, 58.28939006,\n",
      +       "        58.833154  , 61.51840581, 55.25217099, 56.4254845 , 54.7024907 ,\n",
      +       "        56.17677047, 56.04153378, 57.83916418, 55.20599162, 54.27016718,\n",
      +       "        57.05164835, 56.95131941, 58.57929755, 53.19104684, 54.07801109,\n",
      +       "        55.3400961 , 55.65288395, 57.54696984, 57.09434724, 56.22690061,\n",
      +       "        54.21194721, 60.58399367, 58.19419433, 54.90143097, 53.49163023,\n",
      +       "        56.73259815, 57.70021646, 56.11783326, 55.96686744, 55.76571785,\n",
      +       "        55.34804173, 58.66479556, 54.68594097, 54.79734979, 54.95965659,\n",
      +       "        53.64838025, 55.32194173, 57.71806254, 56.54191389, 57.73287538,\n",
      +       "        56.90015515, 55.38550608, 56.59818522, 54.61821393, 55.26335313,\n",
      +       "        54.73477994, 54.15976279, 52.8392555 , 53.48025994, 53.96651396,\n",
      +       "        54.28014372, 52.93113484, 53.09466032, 53.41947117, 54.13099792,\n",
      +       "        54.5052897 , 53.42698137, 54.40697739, 58.33575887, 56.18433882,\n",
      +       "        53.53284898, 57.63800507, 55.19414162, 53.88400699, 53.65503799,\n",
      +       "        52.67474656, 52.52172569, 53.24706809, 54.00025521, 53.89991137,\n",
      +       "        55.02984161, 53.43016807, 53.0520668 , 54.15691284, 55.42878335],\n",
      +       "       [55.3822623 , 59.81056173, 55.64112043, 56.18196229, 55.60043066,\n",
      +       "        53.83059113, 55.18556181, 53.21963065, 53.22559457, 53.46693633,\n",
      +       "        54.62519786, 54.42307762, 54.92188519, 55.34888112, 59.29131549,\n",
      +       "        56.71434891, 56.79993023, 57.56816529, 54.07599827, 55.39216035,\n",
      +       "        53.61094082, 56.27441895, 55.31600539, 53.75741468, 56.62581742,\n",
      +       "        58.18543468, 57.59152655, 56.81623061, 55.27311743, 55.9923049 ,\n",
      +       "        55.15914792, 60.44055013, 61.27605582, 60.65288657, 54.7753763 ,\n",
      +       "        54.42777563, 53.74441914, 53.9477266 , 53.58420238, 54.90389469,\n",
      +       "        53.77882466, 53.72599857, 54.26071386, 52.75018063, 52.45961211,\n",
      +       "        54.52596705, 55.21822139, 57.65914474, 55.30422053, 54.59079862,\n",
      +       "        53.08899651, 54.11246768, 54.59633058, 59.36142273, 57.98447929,\n",
      +       "        55.25600368, 53.01020255, 54.84853433, 55.53882608, 57.62262189,\n",
      +       "        54.91854946, 54.59678057, 55.40082331, 54.1586173 , 54.48159281,\n",
      +       "        54.08301829, 53.93802269, 53.06706389, 53.43069143, 57.7508353 ,\n",
      +       "        54.82736975, 56.2935323 , 55.54100327, 56.68151552, 55.89609696,\n",
      +       "        55.59678816, 54.33260931, 53.78096461, 54.8896869 , 53.10965047,\n",
      +       "        53.49075107, 56.78269406, 54.74626399, 57.2148205 , 61.49089353,\n",
      +       "        61.4739368 , 55.9757647 , 55.84618341, 59.23638773, 55.75793207,\n",
      +       "        54.07217226, 56.80480975, 57.33068601, 53.94287084, 54.96016718,\n",
      +       "        56.69786563, 59.61278391, 54.54744418, 55.32297331, 54.18483462],\n",
      +       "       [54.81980602, 54.54759105, 54.00704264, 56.38890594, 56.22959543,\n",
      +       "        53.61962523, 55.16485708, 56.61596492, 55.42206865, 55.13485761,\n",
      +       "        54.05053445, 54.06903577, 54.36674663, 54.72416376, 56.0394471 ,\n",
      +       "        55.79246701, 56.64045218, 56.51905542, 55.3305415 , 55.21572647,\n",
      +       "        54.54412746, 54.3807672 , 57.96824159, 55.85916977, 53.32922816,\n",
      +       "        54.44885399, 54.49598135, 55.0527619 , 53.68019636, 53.48470965,\n",
      +       "        54.15225954, 54.23972113, 55.38668127, 58.36080842, 59.40270824,\n",
      +       "        59.57999128, 60.67115276, 54.92185354, 54.17786343, 53.52733897,\n",
      +       "        53.7691647 , 55.79727457, 54.96699542, 55.90089762, 53.57343332,\n",
      +       "        52.69594845, 55.85618121, 53.16032756, 57.40359326, 54.87627383,\n",
      +       "        54.73429115, 53.90973697, 57.15613986, 56.28911318, 56.39370077,\n",
      +       "        54.08196216, 53.55390663, 53.47488026, 53.3517827 , 53.54277185,\n",
      +       "        55.48229026, 52.93140303, 53.89564195, 56.04434438, 56.38955193,\n",
      +       "        57.65623982, 56.6401885 , 57.00621682, 54.35458282, 53.82794241,\n",
      +       "        53.61159728, 53.27702327, 53.23833891, 55.92383154, 54.25296688,\n",
      +       "        55.23291818, 55.48720732, 54.34776949, 53.5146859 , 54.33834852,\n",
      +       "        56.71387665, 57.53024085, 56.87244188, 55.47486355, 54.54061168,\n",
      +       "        54.63852628, 55.60969175, 52.75057305, 54.06517225, 57.81892937,\n",
      +       "        56.25295679, 54.87751093, 54.43233857, 53.56604685, 55.06925083,\n",
      +       "        56.99427391, 54.3951293 , 53.94823768, 56.23421743, 55.53056154]])
    • log_likelihood
      (chain, draw, developer)
      float64
      -11.4 -11.42 ... -12.0 -11.87
      array([[[-11.40145445, -11.42031838, -11.52073879, -11.7295851 ,\n",
      +       "         -11.69035476],\n",
      +       "        [-10.53626275, -10.67935024, -11.44497351, -13.03225065,\n",
      +       "         -12.72314184],\n",
      +       "        [-10.53626275, -10.67935024, -11.44497351, -13.03225065,\n",
      +       "         -12.72314184],\n",
      +       "        ...,\n",
      +       "        [-11.06151093, -11.10025127, -11.30744291, -11.73733819,\n",
      +       "         -11.65413021],\n",
      +       "        [-11.36570771, -11.38584033, -11.49354039, -11.71697873,\n",
      +       "         -11.67366656],\n",
      +       "        [-11.03198095, -11.07356611, -11.29538136, -11.75641875,\n",
      +       "         -11.66888514]],\n",
      +       "\n",
      +       "       [[-11.38470511, -11.40439082, -11.50879815, -11.72636764,\n",
      +       "         -11.68651771],\n",
      +       "        [-11.22712952, -11.25431152, -11.39930774, -11.70047072,\n",
      +       "         -11.64306075],\n",
      +       "        [-10.56621843, -10.69701533, -11.39672075, -12.84760729,\n",
      +       "         -12.56556679],\n",
      +       "        ...,\n",
      +       "        [-11.23625872, -11.26270357, -11.40430891, -11.69785887,\n",
      +       "         -11.64051413],\n",
      +       "        [-11.16355868, -11.19424724, -11.35919395, -11.70036784,\n",
      +       "         -11.63202167],\n",
      +       "        [-11.35436805, -11.37552837, -11.48730656, -11.72067037,\n",
      +       "         -11.67904118]],\n",
      +       "\n",
      +       "       [[-11.08898705, -11.12656165, -11.32482003, -11.73852761,\n",
      +       "         -11.66484305],\n",
      +       "        [-10.65336356, -10.75606488, -11.30464923, -12.44422574,\n",
      +       "         -12.22606038],\n",
      +       "        [-10.92678683, -10.97911567, -11.25925004, -11.84037219,\n",
      +       "         -11.72737855],\n",
      +       "        ...,\n",
      +       "        [-11.06206055, -11.1018377 , -11.31196879, -11.75017671,\n",
      +       "         -11.67147269],\n",
      +       "        [-10.67785079, -10.77684503, -11.30031361, -12.39191691,\n",
      +       "         -12.19507418],\n",
      +       "        [-10.65035012, -10.75617206, -11.31733244, -12.48549399,\n",
      +       "         -12.27038183]],\n",
      +       "\n",
      +       "       [[-11.51186232, -11.52669346, -11.6060536 , -11.77062504,\n",
      +       "         -11.73861813],\n",
      +       "        [-10.831398  , -10.89630423, -11.24495084, -11.96671216,\n",
      +       "         -11.82309587],\n",
      +       "        [-10.86651178, -10.92592797, -11.24586809, -11.9073356 ,\n",
      +       "         -11.7736704 ],\n",
      +       "        ...,\n",
      +       "        [-10.93603324, -10.98872934, -11.26735276, -11.84868552,\n",
      +       "         -11.74422492],\n",
      +       "        [-11.54533609, -11.55957134, -11.63467812, -11.79153177,\n",
      +       "         -11.76373546],\n",
      +       "        [-10.83295346, -10.90035112, -11.25603918, -11.99876654,\n",
      +       "         -11.8669146 ]]])
    • lp
      (chain, draw)
      float64
      -53.96 -54.01 ... -55.53 -54.01
      array([[-53.96381729, -54.00782976, -54.00782976, -52.56756903,\n",
      +       "        -53.0149423 , -52.44528159, -52.8077669 , -52.95481785,\n",
      +       "        -53.29050726, -52.17809889, -53.14311051, -53.65740292,\n",
      +       "        -52.87642105, -52.33476269, -53.17958894, -55.14064277,\n",
      +       "        -55.20154663, -53.10580517, -53.99614326, -52.69233002,\n",
      +       "        -52.569215  , -53.76518656, -52.78138382, -53.38130911,\n",
      +       "        -52.85263002, -52.47472048, -52.55388795, -52.97813493,\n",
      +       "        -52.76108093, -54.44070474, -53.69365141, -53.39922724,\n",
      +       "        -52.68406095, -52.86866652, -54.12845355, -53.04799365,\n",
      +       "        -52.96450347, -53.35983186, -52.51955477, -52.49628059,\n",
      +       "        -52.52182286, -52.7832689 , -53.29865416, -57.81489083,\n",
      +       "        -56.90823188, -53.12995727, -52.70042847, -52.9248531 ,\n",
      +       "        -54.77374961, -53.14780218, -52.43919439, -52.54888728,\n",
      +       "        -55.3304341 , -56.11754312, -56.11754312, -56.02559604,\n",
      +       "        -54.93829307, -53.74882296, -52.49524283, -52.29961781,\n",
      +       "        -52.28158833, -52.25475584, -52.2259056 , -52.36642334,\n",
      +       "        -54.60805444, -52.63761948, -53.21542986, -53.45567435,\n",
      +       "        -53.57077851, -53.87929351, -53.32364499, -55.92228379,\n",
      +       "        -54.65072556, -54.5239253 , -52.81912544, -53.80259553,\n",
      +       "        -53.94405651, -52.73413277, -53.05598799, -54.14992967,\n",
      +       "        -53.17367296, -52.80227161, -53.25816981, -52.6483096 ,\n",
      +       "        -53.11186587, -53.4408176 , -52.43856814, -54.22453684,\n",
      +       "        -52.31209868, -53.28773393, -53.17834299, -52.98030364,\n",
      +       "        -53.93357675, -54.43848166, -53.49329004, -55.12078924,\n",
      +       "        -53.84121909, -53.02125483, -53.83654548, -54.21830474],\n",
      +       "       [-54.73950897, -52.84447575, -53.64593501, -54.98537258,\n",
      +       "        -52.43119138, -53.80209799, -53.71171102, -53.3600033 ,\n",
      +       "        -52.79878035, -52.45580196, -52.36808551, -52.70410307,\n",
      +       "        -52.84516061, -54.36851295, -55.52194762, -53.6164185 ,\n",
      +       "        -52.569483  , -52.48811245, -52.56037207, -52.32383185,\n",
      +       "        -52.42090834, -52.56034886, -52.54351631, -54.94861526,\n",
      +       "        -57.96082132, -56.69025539, -53.209137  , -54.7980339 ,\n",
      +       "        -52.81939277, -54.15897139, -53.24011185, -54.83326416,\n",
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      +       "        0.96510997, 0.96510997, 0.96510997, 0.96510997, 0.96510997,\n",
      +       "        0.96510997, 0.96510997, 0.96510997, 0.96510997, 0.96510997,\n",
      +       "        0.96510997, 0.96510997, 0.96510997, 0.96510997, 0.96510997,\n",
      +       "        0.96510997, 0.96510997, 0.96510997, 0.96510997, 0.96510997,\n",
      +       "        0.96510997, 0.96510997, 0.96510997, 0.96510997, 0.96510997,\n",
      +       "        0.96510997, 0.96510997, 0.96510997, 0.96510997, 0.96510997,\n",
      +       "        0.96510997, 0.96510997, 0.96510997, 0.96510997, 0.96510997,\n",
      +       "        0.96510997, 0.96510997, 0.96510997, 0.96510997, 0.96510997,\n",
      +       "        0.96510997, 0.96510997, 0.96510997, 0.96510997, 0.96510997,\n",
      +       "        0.96510997, 0.96510997, 0.96510997, 0.96510997, 0.96510997,\n",
      +       "        0.96510997, 0.96510997, 0.96510997, 0.96510997, 0.96510997,\n",
      +       "        0.96510997, 0.96510997, 0.96510997, 0.96510997, 0.96510997,\n",
      +       "        0.96510997, 0.96510997, 0.96510997, 0.96510997, 0.96510997,\n",
      +       "        0.96510997, 0.96510997, 0.96510997, 0.96510997, 0.96510997,\n",
      +       "        0.96510997, 0.96510997, 0.96510997, 0.96510997, 0.96510997,\n",
      +       "        0.96510997, 0.96510997, 0.96510997, 0.96510997, 0.96510997,\n",
      +       "        0.96510997, 0.96510997, 0.96510997, 0.96510997, 0.96510997,\n",
      +       "        0.96510997, 0.96510997, 0.96510997, 0.96510997, 0.96510997,\n",
      +       "        0.96510997, 0.96510997, 0.96510997, 0.96510997, 0.96510997,\n",
      +       "        0.96510997, 0.96510997, 0.96510997, 0.96510997, 0.96510997,\n",
      +       "        0.96510997, 0.96510997, 0.96510997, 0.96510997, 0.96510997,\n",
      +       "        0.96510997, 0.96510997, 0.96510997, 0.96510997, 0.96510997,\n",
      +       "        0.96510997, 0.96510997, 0.96510997, 0.96510997, 0.96510997,\n",
      +       "        0.96510997, 0.96510997, 0.96510997, 0.96510997, 0.96510997,\n",
      +       "        0.96510997, 0.96510997, 0.96510997, 0.96510997, 0.96510997,\n",
      +       "        0.96510997, 0.96510997, 0.96510997, 0.96510997, 0.96510997,\n",
      +       "        0.96510997, 0.96510997, 0.96510997, 0.96510997, 0.96510997,\n",
      +       "        0.96510997, 0.96510997, 0.96510997, 0.96510997, 0.96510997,\n",
      +       "        0.96510997, 0.96510997, 0.96510997, 0.96510997, 0.96510997]])
    • b1
      (chain, draw)
      float64
      -1.508 -1.508 ... -1.508 -1.508
      array([[-1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537,\n",
      +       "        -1.50807537, -1.50807537, -1.50807537, -1.50807537, -1.50807537]])
    • log_sigma
      (chain, draw)
      float64
      -1.05 -1.05 -1.05 ... -1.05 -1.05
      array([[-1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636,\n",
      +       "        -1.0495636, -1.0495636, -1.0495636, -1.0495636, -1.0495636]])
    • sigma
      (chain, draw)
      float64
      0.3501 0.3501 ... 0.3501 0.3501
      array([[0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049,\n",
      +       "        0.35009049, 0.35009049, 0.35009049, 0.35009049, 0.35009049]])
    • log_lik
      (chain, draw, developer)
      float64
      -2.298e+08 ... -3.091e+09
      array([[[-2.29829515e+08, -4.16818509e+08, -1.41280767e+09,\n",
      +       "         -3.48244709e+09, -3.09101610e+09],\n",
      +       "        [-2.29829515e+08, -4.16818509e+08, -1.41280767e+09,\n",
      +       "         -3.48244709e+09, -3.09101610e+09],\n",
      +       "        [-2.29829515e+08, -4.16818509e+08, -1.41280767e+09,\n",
      +       "         -3.48244709e+09, -3.09101610e+09],\n",
      +       "        [-2.29829515e+08, -4.16818509e+08, -1.41280767e+09,\n",
      +       "         -3.48244709e+09, -3.09101610e+09],\n",
      +       "        [-2.29829515e+08, -4.16818509e+08, -1.41280767e+09,\n",
      +       "         -3.48244709e+09, -3.09101610e+09],\n",
      +       "        [-2.29829515e+08, -4.16818509e+08, -1.41280767e+09,\n",
      +       "         -3.48244709e+09, -3.09101610e+09],\n",
      +       "        [-2.29829515e+08, -4.16818509e+08, -1.41280767e+09,\n",
      +       "         -3.48244709e+09, -3.09101610e+09],\n",
      +       "        [-2.29829515e+08, -4.16818509e+08, -1.41280767e+09,\n",
      +       "         -3.48244709e+09, -3.09101610e+09],\n",
      +       "        [-2.29829515e+08, -4.16818509e+08, -1.41280767e+09,\n",
      +       "         -3.48244709e+09, -3.09101610e+09],\n",
      +       "        [-2.29829515e+08, -4.16818509e+08, -1.41280767e+09,\n",
      +       "         -3.48244709e+09, -3.09101610e+09],\n",
      +       "        [-2.29829515e+08, -4.16818509e+08, -1.41280767e+09,\n",
      +       "         -3.48244709e+09, -3.09101610e+09],\n",
      +       "        [-2.29829515e+08, -4.16818509e+08, -1.41280767e+09,\n",
      +       "         -3.48244709e+09, -3.09101610e+09],\n",
      +       "        [-2.29829515e+08, -4.16818509e+08, -1.41280767e+09,\n",
      +       "         -3.48244709e+09, -3.09101610e+09],\n",
      +       "        [-2.29829515e+08, -4.16818509e+08, -1.41280767e+09,\n",
      +       "         -3.48244709e+09, -3.09101610e+09],\n",
      +       "        [-2.29829515e+08, -4.16818509e+08, -1.41280767e+09,\n",
      +       "         -3.48244709e+09, -3.09101610e+09],\n",
      +       "        [-2.29829515e+08, -4.16818509e+08, -1.41280767e+09,\n",
      +       "         -3.48244709e+09, -3.09101610e+09],\n",
      +       "        [-2.29829515e+08, -4.16818509e+08, -1.41280767e+09,\n",
      +       "         -3.48244709e+09, -3.09101610e+09],\n",
      +       "        [-2.29829515e+08, -4.16818509e+08, -1.41280767e+09,\n",
      +       "         -3.48244709e+09, -3.09101610e+09],\n",
      +       "        [-2.29829515e+08, -4.16818509e+08, -1.41280767e+09,\n",
      +       "         -3.48244709e+09, -3.09101610e+09],\n",
      +       "        [-2.29829515e+08, -4.16818509e+08, -1.41280767e+09,\n",
      +       "         -3.48244709e+09, -3.09101610e+09],\n",
      +       "        [-2.29829515e+08, -4.16818509e+08, -1.41280767e+09,\n",
      +       "         -3.48244709e+09, -3.09101610e+09],\n",
      +       "        [-2.29829515e+08, -4.16818509e+08, -1.41280767e+09,\n",
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  • created_at :
    2019-11-10T20:53:29.366357
    inference_library :
    pystan
    inference_library_version :
    2.19.1.1
" + ], + "text/plain": [ + "\n", + "Dimensions: (chain: 1, developer: 5, draw: 200)\n", + "Coordinates:\n", + " * chain (chain) int64 0\n", + " * draw (draw) int64 0 1 2 3 4 5 6 ... 194 195 196 197 198 199\n", + " * developer (developer) object 'Alice' 'Bob' ... 'Danielle' 'Erika'\n", + "Data variables:\n", + " slack_comments_hat (chain, draw, developer) float64 -5.736 ... -26.45\n", + "Attributes:\n", + " created_at: 2019-11-10T20:53:29.366357\n", + " inference_library: pystan\n", + " inference_library_version: 2.19.1.1" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "idata_stan.prior_predictive" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.8" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/schema/linear_regression_data.csv b/schema/linear_regression_data.csv new file mode 100644 index 0000000000..19d6d91594 --- /dev/null +++ b/schema/linear_regression_data.csv @@ -0,0 +1,6 @@ +,comments,time +Alice,7500,4.5 +Bob,10100,6.0 +Cole,18600,7.0 +Danielle,29200,12.0 +Erika,27500,18.0 From 436f4ebb0e5c61329fce6988b1d0f48bdca5e9ca Mon Sep 17 00:00:00 2001 From: "Oriol (Prodesk)" Date: Sun, 10 Nov 2019 22:49:52 +0100 Subject: [PATCH 5/6] Continue writing schema.md Added example section, added toc, fixed many comments --- schema.md | 52 ++++++++++++++++++++++++++++++++++++++-------------- 1 file changed, 38 insertions(+), 14 deletions(-) diff --git a/schema.md b/schema.md index d5625ff8f5..cfbc3dc4c4 100644 --- a/schema.md +++ b/schema.md @@ -1,7 +1,7 @@ # InferenceData schema specification The `InferenceData` schema scheme defines a data structure compatible with [NetCDF](https://www.unidata.ucar.edu/software/netcdf/) with 3 goals in mind, usefulness in the analysis of Bayesian inference results, reproducibility of Bayesian inference analysis and interoperability between different inference backends and programming languages. -Currently there are 2 implementations of this design: +Currently there are 2 beta implementations of this design: * [ArviZ](https://arviz-devs.github.io/arviz/) in Python which integrates with: - [emcee](https://emcee.readthedocs.io/en/stable/) - [PyMC3](https://docs.pymc.io) @@ -12,12 +12,28 @@ Currently there are 2 implementations of this design: and [CmdStanPy](https://cmdstanpy.readthedocs.io/en/latest/index.html) - [tensorflow-probability](https://www.tensorflow.org/probability) * [ArviZ.jl](https://github.com/sethaxen/ArviZ.jl) in Julia which integrates with: - - [Turing](https://turing.ml/dev/). + - [Turing.jl](https://turing.ml/dev/) and indirectly any package using [MCMCChains.jl](https://github.com/TuringLang/MCMCChains.jl) to store results + - [CmdStan.jl](https://github.com/StanJulia/CmdStan.jl), [StanSample.jl](https://github.com/StanJulia/StanSample.jl) and [Stan.jl](https://github.com/StanJulia/Stan.jl) + +## Contents +1. [Current design](#current-design) + 1. [`posterior`](#posterior) + 1. [`sample_stats`](#sample_stats) + 1. [`posterior_predictive`](#posterior_predictive) + 1. [`observed_data`](#observed_data) + 1. [`constant_data`](#constant_data) + 1. [`prior`](#prior) + 1. [`sample_stats_prior`](#sample_stats_prior) + 1. [`prior_predictive`](#prior_predictive) +1. [Planned features](#planned-features) + 1. [Sampler parameters](#sampler-parameters) + 1. [Out of sample posterior_predictive samples](#Out-of-sample-posterior-predictive-samples) +1. [Examples](#examples) ## Current design `InferenceData` stores all quantities relevant in order to fulfill its goals in different groups. Each group, described below, stores a conceptually different quantity generally represented by several multidimensional labeled variables. -Each group should have one entry per variable, with the first two dimensions of each variable should be the sample identifier (`chain`, `draw`). Dimensions must be named and explicit their index values, called coordinates. Coordinates can have repeated identifiers and may not be numerical. Variable names must not share names with dimensions. +Each group should have one entry per variable. When relevant, the first two dimensions of each variable should be the sample identifier (`chain`, `draw`). For groups like `observed_data` or `constant_data` these two initial dimensions are omitted. Dimensions must be named and specify their index values, called coordinates. Coordinates can have repeated identifiers and may not be numerical. Variable names must not share names with dimensions. Moreover, each group contains the following attributes: * `created_at`: the date of creation of the group. @@ -30,8 +46,8 @@ Moreover, each group contains the following attributes: Samples from the posterior distribution p(theta|y). #### `sample_stats` -Information and diagnostics about each `posterior` sample, provided by the inference backend. It may vary depending on the algorithm used by the backend (i.e. an affine invariant sampler has no energy associated). The name convention used for `sample_stats` variables is the following: -* `lp`: unnormalized log probability of the sample +Information and diagnostics for each `posterior` sample, provided by the inference backend. It may vary depending on the algorithm used by the backend (i.e. an affine invariant sampler has no energy associated). The name convention used for `sample_stats` variables is the following: +* `lp`: (unnormalized) log probability for sample * `step_size` * `step_size_bar` * `tune`: boolean variable indicating if the sampler is tuning or sampling @@ -43,21 +59,23 @@ Information and diagnostics about each `posterior` sample, provided by the infer * `energy_error` * `max_energy_error` -#### `observed_data` -Observed data on which the `posterior` is conditional. It should only contain data which is modeled as a random variable. Each variable should have a counterpart in `posterior_predictive`. The `posterior_predictive` counterpart variable may have a different name. - #### `posterior_predictive` -Posterior predictive samples p(y|y) corresponding to the posterior predictive pdf evaluated at the `observed_data`. Samples should match with `posterior` ones and each variable should have a counterpart in `observed_data`. The `observed_data` counterpart variable may have a different name. +Posterior predictive samples p(y|y) corresponding to the posterior predictive distribution evaluated at the `observed_data`. Samples should match with `posterior` ones and each variable should have a counterpart in `observed_data`. The `observed_data` counterpart variable may have a different name. + +#### `observed_data` +Observed data on which the `posterior` is conditional. It should only contain data which is modeled as a random variable. Each variable should have a counterpart in `posterior_predictive`, however, the `posterior_predictive` counterpart variable may have a different name. #### `constant_data` -Model constants, data included in the model which is not modeled as a random variable (i.e. the x in a linear regression). It should be the data used to generate the `posterior` and `posterior_predictive` samples. +Model constants, data included in the model which is not modeled as a random variable. It should be the data used to generate the `posterior` and `posterior_predictive` samples. #### `prior` -p(theta) +Samples from the prior distribution p(theta). Samples should not match `posterior` samples. However, this group will still follow the convention on `chain` and `draw` as first dimensions. Each variable should have a counterpart in `posterior`. #### `sample_stats_prior` +Information and diagnostics for each `prior` sample, provided by the inference backend. It may vary depending on the algorithm used by the backend (i.e. an affine invariant sampler has no energy associated). Variable names follow the same convention defined in [`sample_stats`](#sample_stats). #### `prior_predictive` +Samples from the prior predictive distribution. Samples should match `prior` samples and each variable should have a counterpart in `posterior_predictive`/`observed_data`. ## Planned features @@ -65,7 +83,13 @@ p(theta) ### Out of sample posterior_predictive samples #### `predictions` -Out of sample posterior predictive samples p(y'|y). +Out of sample posterior predictive samples p(y'|y). Sample should match `posterior` samples. Its variables should have a counterpart in `posterior_predictive`. However, variables in `predictions` and their counterpart in `posterior_predictive` may not share coordinated. + +#### `predictions_constant_data` +Model constants used to get the `predictions` samples. Its variables should have a counterpart in `constant_data`. However, variables in `predictions_constant_data` and their counterpart in `constant_data` may not share coordinates. -#### `constant_data_predictions` -Model constants used to get the `predictions` samples. Its variables should have a counterpart in `constant_data`. +## Examples +In order to clarify the definitions above, an example of `InferenceData` generation for a 1D linear regression is available in several programming languages and probabilistic programming frameworks. This particular inference task has been chosen because it is widely well known while still being very useful and it also allows to populate all the fields in the `InferenceData` object. +* Python + - PyMC3 + - [PyStan](schema/PyStan_schema_example.ipynb) From 3a3fe9c2404108dd60289f650232e48d8d315cde Mon Sep 17 00:00:00 2001 From: "Oriol (Prodesk)" Date: Sun, 10 Nov 2019 23:16:51 +0100 Subject: [PATCH 6/6] typo --- schema.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/schema.md b/schema.md index cfbc3dc4c4..7dbc9391aa 100644 --- a/schema.md +++ b/schema.md @@ -27,7 +27,7 @@ Currently there are 2 beta implementations of this design: 1. [`prior_predictive`](#prior_predictive) 1. [Planned features](#planned-features) 1. [Sampler parameters](#sampler-parameters) - 1. [Out of sample posterior_predictive samples](#Out-of-sample-posterior-predictive-samples) + 1. [Out of sample posterior_predictive samples](#out-of-sample-posterior_predictive-samples) 1. [Examples](#examples) ## Current design