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| # 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. | ||
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| / | ||
| 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/). | ||
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| attrs: | ||
| backend: "stan" or "pymc3" | ||
| version: str | ||
| model_name?: str | ||
| comment?: str | ||
| model_version?: str | ||
| timestamp: int | ||
| author?: str | ||
| ## 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. | ||
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| /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. | ||
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| /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. | ||
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| /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. | ||
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| /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). | ||
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| /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` | ||
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| /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. | ||
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| /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. | ||
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| /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. | ||
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| /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) | ||
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| /prior? | ||
| Samples from the prior distribution. Same shapes as in trace. (except for (sample, chain)) | ||
| #### `sample_stats_prior` | ||
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| /prior_predictive? | ||
| Samples from the prior predictive distribution. Same vars as in /data | ||
| #### `prior_predictive` | ||
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| /posterior_predictive? | ||
| Samples from the posterior predicitve distribution. Same vars as in /data | ||
| ## Planned features | ||
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| /trace | ||
| TODO We could call this /posterior | ||
| ### Sampler parameters | ||
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| 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). | ||
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| /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. | ||
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| Variable names must not share names with coordinate names. | ||
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| 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? | ||
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| 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`. |
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