A Python library for analysing cmdstanpy output

This is a collection of functions for analysing output of cmdstanpy library. The main idea is to do a quick data analysis by calling a single function that makes:

• traceplots of samples,

• text and plots of the summaries of model parameters,

• histograms and pair plots of posterior distributions of parameters.

The only known illustration of a tarpan made from life, depicting a five month old colt (Borisov, 1841). Source: Wikimedia Commons.

Setup

First, run:

pip install tarpan

Finally, install cmdstan by running:

install_cmdstan

Complete analysis: save_analysis

This is the main function of the library that saves summaries and trace/pair/tree plots in model_info directory. The function is useful when you want to generate all types of summaries and plots at once.

from tarpan.cmdstanpy.analyse import save_analysis

model = CmdStanModel(stan_file="your_model.stan")
fit = model.sample(data=your_data)
save_analysis(fit, param_names=['mu', 'sigma'])

• Full example code

If you don't need everything, you can call individual functions described below to make just one type of plot or a summary.

Analysis without cmdstanpy

Here is how to analyse values from Pandas' data frame columns:

from tarpan.shared.analyse import save_analysis
save_analysis(df, param_names=['mu', 'sigma'])

• Full example code

Summary: save_summary

Creates a summary of parameter distributions and saves it in text and CSV files.

from tarpan.cmdstanpy.summary import save_summary

model = CmdStanModel(stan_file="your_model.stan")
fit = model.sample(data=your_data)
save_summary(fit, param_names=['mu', 'tau', 'eta.1'])

• Full example code

• Call print_summary to print summary to console instead of saving to a file.

The text summary format is such that the text can be pasted into Github/Gitlab/Bitbucket's Markdown file, like this:

Name	Mean	Std	Mode	+	-	68CI-	68CI+	95CI-	95CI+	N_Eff	R_hat
mu	8.05	5.12	7.53	4.63	4.59	2.93	12.16	-1.84	18.74	1540	1.00
tau	6.41	5.72	2.36	5.41	2.35	0.00	7.76	0.00	17.07	1175	1.00
eta.1	0.39	0.92	0.60	0.71	1.13	-0.53	1.31	-1.48	2.19	3505	1.00

Summary columns

• Name, Mean, Std are the name of the parameter, its mean and standard deviation.

• 68CI-, 68CI+, 95CI-, 95CI+ are the 68% and 95% HPDIs (highest posterior density intervals). These values are configurable.

• Mode, +, - is a mode of distribution with upper and lower uncertainties, which are calculated as distances to 68% HPDI.

• N_Eff is Stan's number of effective samples, the higher the better.

• R_hat is a Stan's parameter representing the quality of the sampling. This value needs to be around 1.00. After generating a model I usually immediately look at this R_hat column to see if the sampling was good.

Summary without cmdstanpy

Here is how to make summary of values from Pandas' data frame columns:

from tarpan.shared.summary import save_summary
save_summary(df, param_names=['mu', 'sigma'])

• Full example code

Tree plot: save_tree_plot

This function shows exactly the same information as save_summary, but in the form of a plot. The markers are the modes of the distributions, and the two error bars indicate 68% and 95% HPDIs (highest posterior density intervals).

from tarpan.cmdstanpy.tree_plot import save_tree_plot

model = CmdStanModel(stan_file="your_model.stan")
fit = model.sample(data=your_data)
save_tree_plot([fit], param_names=['mu', 'sigma'])

• Full example code

Tree plot without cmdstanpy

One can make a tree plot by supplying a Panda's data frame that shows summaries of values for the frame's columns:

from tarpan.shared.tree_plot import save_tree_plot
save_tree_plot([df], param_names=['mu', 'sigma'])

• Full example code

Comparing multiple models on a tree plot

Supply multiple fits in order to compare parameters from multiple models.

from tarpan.cmdstanpy.tree_plot import save_tree_plot
from tarpan.shared.tree_plot import TreePlotParams

# Sample from two models
model1 = CmdStanModel(stan_file="your_model1.stan")
fit1 = model1.sample(data=your_data)
model2 = CmdStanModel(stan_file="your_model2.stan")
fit2 = model2.sample(data=your_data)

# Supply legend labels (optional)
tree_params = TreePlotParams()
tree_params.labels = ["Model 1", "Model 2", "Exact"]
data = [{"mu": 2.2, "tau": 1.3}]  # Add extra markers (optional)

save_tree_plot([fit1, fit2], extra_values=data, param_names=['mu', 'tau'],
               tree_params=tree_params)

• Full example code

Comparing parameters of multiple models

Use save_compare_parameters function to compare parameters between different models:

	mu	tau
Model 1	7.53 (+4.63, -4.59)	2.36 (+5.41, -2.35)
Model 2	8.87 (+9.05, -9.50)	3.64 (+8.14, -3.61)

This table is a numerical version of the plot created by save_tree_plot. The values here are modes of the distributions and uncertainties are distances to 68% HPD intervals.

from tarpan.cmdstanpy.compare_parameters import save_compare_parameters
extra = [{"mu": 2.2, "theta": 1.3}]  # Add extra values (optional)

save_compare_parameters([fit1, fit2], labels=['Model 1', 'Model 2', 'Extra'],
                        extra_values=extra,
                        param_names=["mu", "theta"])

• Full example code

Use save_compare_parameters without cmdstanpy

Here is how to compare parameters using Pandas data frames df1 and df2:

from tarpan.shared.compare_parameters import save_compare_parameters
extra = [{"mu": 2.2, "theta": 1.3}]  # Add extra values (optional)

save_compare_parameters([df1, df2], labels=['Model 1', 'Model 2', 'Extra'],
                        extra_values=extra,
                        param_names=["mu", "theta"])

• Full example code

Trace plot: save_traceplot

The plot shows the values of parameters samples. Different colors correspond to samples form different chains. Ideally, the lines of different colors on the left plots are well mixed, and the right plot is fairly uniform.

from tarpan.cmdstanpy.traceplot import save_traceplot

model = CmdStanModel(stan_file="your_model.stan")
fit = model.sample(data=your_data)
save_traceplot(fit, param_names=['mu', 'tau', 'eta.1'])

• Full example code

Pair plot: save_pair_plot

The plot helps to see correlations between parameters and spot funnel shaped distributions that can result in sampling problems.

from tarpan.cmdstanpy.pair_plot import save_pair_plot
model = CmdStanModel(stan_file="your_model.stan")
fit = model.sample(data=your_data)
save_pair_plot(fit, param_names=['mu', 'tau', 'eta.1'])

• Full example code

Pair plot without cmdstanpy

Here is how to make a pair plot of values from Pandas' data frame columns:

from tarpan.shared.pair_plot import save_pair_plot
save_pair_plot(df, param_names=['mu', 'sigma'])

• Full example code

Histogram: save_histogram

Show histograms of parameter distributions.

from tarpan.cmdstanpy.histogram import save_histogram
model = CmdStanModel(stan_file="your_model.stan")
fit = model.sample(data=your_data)
save_histogram(fit, param_names=['mu', 'tau', 'eta.1', 'theta.1'])

• Full example code

Histogram without cmdstanpy

Here is how to make histograms of values from Pandas' data frame columns:

from tarpan.shared.histogram import save_histogram
save_histogram(df, param_names=['mu', 'sigma'])

• Full example code

Comparing models

Run save_compare to compare multiple models using WAIC and PSIS methods in order to see which models are more compatible with the data.

from tarpan.cmdstanpy.compare import save_compare

model1 = CmdStanModel(stan_file="your_model1.stan")
fit1 = model1.sample(data=your_data)
model2 = CmdStanModel(stan_file="your_model2.stan")
fit2 = model2.sample(data=your_data)

models = {
    "Model": fit1,
    "Another model": fit2
}

save_compare(models=models, lpd_column_name="lpd_pointwise")

Here the lpd_column_name parameter takes the name of the array variable from the generated quantities block that contains log probability densities of all data points.

• Full example code

WAIC and PSIS plots

The save_compare function will create the plots showing WAIC and PSIS values (red round markers). The lower WAIC and PSIS values mean the model is more compatible with the data. The blue triangle marker shows the difference between the model and the best model. The error bars correspond to standard errors.

Numerical summaries for WAIC and PSIS

The save_compare function will also create text and csv files which are text versions of the above plots.

Summary columns are:

• PSIS/WAIC, SE: PSIS and WAIC values and their standard errors.

• dPSIS/dWAIC, dSE: The difference of PSIS and WAIC from the best model (i.e. model with lowest WAIC/PSIS) and the standard error of this difference.

• pWAIC/pPSIS: the penalty (aka effective number of parameters). The purpose of number is to combat overfitting. Penalties are already included in the WAIC/PSIS numbers, so models with too many parameters will have larger penalties, and therefore, larger WAIC/PSIS values.

• Weight: Very approximate measure of the relevance of the model, with higher numbers correspond to models that are more compatible with the data. Since this number is approximate and does not have uncertainty, it's better to use dWAIC/dPSIS with dSE to compare models.

• MaxK: The maximum value of Pareto K parameter from the observations. If this value is above 0.5, and especially above 0.7, the PSIS/WAIC model comparisons might not be reliable.

WAIC summary

	WAIC	SE	dWAIC	dSE	pWAIC	Weight
Fungus+treatment	361.48	13.36			3.49	1.00
Treatment	402.68	10.66	41.20	9.82	2.53	0.00
Intercept	405.88	11.29	44.40	11.56	1.53	0.00

PSIS summary

	PSIS	SE	dPSIS	dSE	pPSIS	MaxK	Weight
Fungus+treatment	361.48	13.36			3.49	0.25	1.00
Treatment	402.69	10.67	41.21	9.82	2.54	0.33	0.00
Intercept	405.88	11.29	44.40	11.56	1.53	0.28	0.00

Plots of Pareto K values

The save_compare function creates plots of Pareto K values for data points. Points with Pareto K values higher than 0.7 are highlighted in red, with their indices shown below the markers. The red points are the ones that have large influence on the model. Having points above 0.7 could mean that WAIC and PSIS are failing and their results should be used with caution and large neon coloured disclaimers.

Saving cmdstan samples to disk

It saves a lot of time to sample the model and save the results to disk, so they can be used on the next run instead of waiting for the sampling again. This can be done with run function:

from tarpan.cmdstanpy.cache import run

# Your function that creates CmdStanModel, runs its `sample` method
# and returns the result.
#
# This function must take `output_dir` input parameter and pass it to `sample`.
#
# It may also have any other parameters you wish to pass from `run`.
def run_stan(output_dir, other_param):
    model = CmdStanModel(stan_file="my_model.stan")

    fit = model.sample(
        data=data,
        output_dir=output_dir  # Pass to make CSVs in correct location
    )

    return fit  # Return the fit

# Will run `run_stan` once, save model to disk and read it on next calls
fit = run(func=run_stan, other_param="some data")

• Full example code

Scatter and KDE plot

The save_scatter_and_kde function saves a scatter and corresponding KDE (kernel density estimate) plot. The KDE plot takes into account uncertainties of individual values:

from tarpan.plot.kde import save_scatter_and_kde

values1 = [
        -0.99, -1.37, -1.38, -1.51, -1.29, -1.34, -1.50, -0.93, -0.83,
        -1.46, -1.07, -1.28, -0.73]

uncertainties1 = [
         0.12,  0.05,  0.11,  0.18,  0.03,  0.19,  0.18,  0.12,  0.19,
         0.09,  0.11,  0.16,  0.08]

values2 = [
        -1.22, -1.15, -0.97, -0.68, -0.37, -0.48, -0.73, -0.61, -1.32,
        -0.62, -1.13, -0.65, -0.90, -1.29, -1.19, -0.54, -0.64, -0.45,
        -1.21, -0.75, -0.66, -0.71, -0.61, -0.59, -1.07, -0.65, -0.59]

uncertainties2 = [
         0.13,  0.14,  0.17,  0.07,  0.11,  0.12,  0.23,  0.05,  0.04,
         0.30,  0.11,  0.13,  0.16,  0.03,  0.18,  0.20,  0.16,  0.16,
         0.11,  0.09,  0.20,  0.10,  0.08,  0.04,  0.04,  0.23,  0.19]

save_scatter_and_kde(values=[values1, values2],
                     uncertainties=[uncertainties1, uncertainties2],
                     title="Sodium abundances in RGB stars of NGC 288",
                     xlabel="Sodium abundance [Na/H]",
                     ylabel=["Star number", "Probability density"],
                     legend_labels=["AGB", "RGB"])

gaussian_kde function

The function returns the values for a KDE plot, taking into account uncertainties of individual values:

from tarpan.plot.kde import gaussian_kde
import numpy as np
import matplotlib.pyplot as plt

x = np.linspace(0, 1, 100)
y = gaussian_kde(x, values, uncert)
plt.fill_between(x, y)

Make posterior-scatter-kde plot

The save_posterior_scatter_and_kde function makes a scatter-KDE plots of the data, same as save_scatter_and_kde. In addition, it plots the posterior distributions.

from tarpan.plot.posterior import save_posterior_scatter_and_kde

# Plot one sample from posterior distribution
def model_pdf(x, row):
    mu = row['mu.1']
    sigma = row['sigma']

    return stats.norm.pdf(x, mu, sigma)


fig, axes = save_posterior_scatter_and_kde(
    fits=[fit1, fit2],  # Two models returned by model.sample function
    pdf=model_pdf,  # Function that plot posterior distribution
    values=[data1["y"], data2["y"]],
    uncertainties=[data1["uncertainties"], data2["uncertainties"]],
    title="Sodium abundances in RGB stars of NGC 288",
    xlabel="Sodium abundance [Na/H]",
    ylabel=["Star number", "Probability density"],
    legend_labels=["AGB", "RGB"])

• Full example code

Common questions

• How to change the widths of HPD intervals?

• Where are plot/summary files placed and how to change that?

Run unit tests

pytest

The unlicense

This work is in public domain.

🐴🐴🐴

This work is dedicated to Tarpan, an extinct subspecies of wild horse.

Special thanks to Richard McElreath, who wrote Statistical Rethinking textbook, as well as Stan and arviz people.