arviz_plots.plot_loo_pit

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arviz_plots.plot_loo_pit#

arviz_plots.plot_loo_pit(dt, ci_prob=0.99, coverage=False, var_names=None, filter_vars=None, group='posterior_predictive', coords=None, sample_dims=None, plot_collection=None, backend=None, labeller=None, aes_by_visuals=None, visuals=None, stats=None, **pc_kwargs)[source]#

LOO-PIT Δ-ECDF values with simultaneous confidence envelope.

For a calibrated model the LOO Probability Integral Transform (PIT) values, $p(tilde{y}_i le y_i mid y_{-i})$, should be uniformly distributed. Where $y_i$ represents the observed data for index $i$ and $tilde y_i$ represents the posterior predictive sample at index $i$. $y_{-i}$ indicates we have left out the $i$-th observation. LOO-PIT values are computed using the PSIS-LOO-CV method described in [1] and [2].

This plot shows the empirical cumulative distribution function (ECDF) of the LOO-PIT values. To make the plot easier to interpret, we plot the Δ-ECDF, that is, the difference between the observed ECDF and the expected CDF. Simultaneous confidence bands are computed using the method described in described in [3].

Alternatively, we can visualize the coverage of the central posterior credible intervals by setting coverage=True. This allows us to assess whether the credible intervals includes the observed values. We can obtain the coverage of the central intervals from the LOO-PIT by replacing the LOO-PIT with two times the absolute difference between the LOO-PIT values and 0.5.

For more details on how to interpret this plot, see https://arviz-devs.github.io/EABM/Chapters/Prior_posterior_predictive_checks.html#pit-ecdfs.

Parameters:
dtxarray.DataTree

Input data

ci_probfloat

Indicates the probability that should be contained within the plotted credible interval. Defaults to 0.99.

coveragebool, optional

If True, plot the coverage of the central posterior credible intervals. Defaults to False.

var_namesstr or list of str, optional

One or more variables to be plotted. Currently only one variable is supported. Prefix the variables by ~ when you want to exclude them from the plot.

filter_vars{None, “like”, “regex”}, optional, default=None

If None (default), interpret var_names as the real variables names. If “like”, interpret var_names as substrings of the real variables names. If “regex”, interpret var_names as regular expressions on the real variables names.

coordsdict, optional

Coordinates to plot.

sample_dimsstr or sequence of hashable, optional

Dimensions to reduce unless mapped to an aesthetic. Defaults to rcParams["data.sample_dims"]

plot_collectionPlotCollection, optional
backend{“matplotlib”, “bokeh”, “plotly”}, optional
labellerlabeller, optional
aes_by_visualsmapping of {strsequence of str}, optional

Mapping of visuals to aesthetics that should use their mapping in plot_collection when plotted. Valid keys are the same as for visuals.

visualsmapping of {strmapping or bool}, optional

Valid keys are:

statsmapping, optional

Valid keys are:

  • ecdf_pit -> passed to ecdf_pit. Default is {"n_simulation": 1000}.

**pc_kwargs

Passed to arviz_plots.PlotCollection.grid

Returns:
PlotCollection

References

[1]

Vehtari et al. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Statistics and Computing. 27(5) (2017) https://doi.org/10.1007/s11222-016-9696-4

[2]

Vehtari et al. Pareto Smoothed Importance Sampling. Journal of Machine Learning Research, 25(72) (2024) https://jmlr.org/papers/v25/19-556.html

[3]

Säilynoja et al. Graphical test for discrete uniformity and its applications in goodness-of-fit evaluation and multiple sample comparison. Statistics and Computing 32(32). (2022) https://doi.org/10.1007/s11222-022-10090-6

Examples

Plot the ecdf-PIT for the crabs hurdle-negative-binomial dataset.

>>> from arviz_plots import plot_loo_pit, style
>>> style.use("arviz-variat")
>>> from arviz_base import load_arviz_data
>>> dt = load_arviz_data('radon')
>>> plot_loo_pit(dt)
../../_images/arviz_plots-plot_loo_pit-1.png

Plot the coverage for the crabs hurdle-negative-binomial dataset.

>>> plot_loo_pit(dt, coverage=True)
../../_images/arviz_plots-plot_loo_pit-2.png

Plot of the probability integral transform of the posterior predictive distribution with respect to the observed data using the leave-one-out (LOO) method.

LOO-PIT ECDF

LOO-PIT ECDF
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