arviz.plot_bpv(data, kind='u_value', t_stat='median', bpv=True, plot_mean=True, reference='analytical', mse=False, n_ref=100, hdi_prob=0.94, color='C0', grid=None, figsize=None, textsize=None, labeller=None, data_pairs=None, var_names=None, filter_vars=None, coords=None, flatten=None, flatten_pp=None, ax=None, backend=None, plot_ref_kwargs=None, backend_kwargs=None, group='posterior', show=None)[source]#

Plot Bayesian p-value for observed data and Posterior/Prior predictive.

dataaz.InferenceData object

arviz.InferenceData object containing the observed and posterior/prior predictive data.


Type of plot to display (“p_value”, “u_value”, “t_stat”). Defaults to u_value. For “p_value” we compute p := p(y* ≤ y | y). This is the probability of the data y being larger or equal than the predicted data y*. The ideal value is 0.5 (half the predictions below and half above the data). For “u_value” we compute pi := p(yi* ≤ yi | y). i.e. like a p_value but per observation yi. This is also known as marginal p_value. The ideal distribution is uniform. This is similar to the LOO-pit calculation/plot, the difference is than in LOO-pit plot we compute pi = p(yi* r ≤ yi | y-i ), where y-i, is all other data except yi. For “t_stat” we compute := p(T(y)* ≤ T(y) | y) where T is any test statistic. See t_stat argument below for details of available options.

t_statstr, float, or callable

Test statistics to compute from the observations and predictive distributions. Allowed strings are “mean”, “median” or “std”. Defaults to “median”. Alternative a quantile can be passed as a float (or str) in the interval (0, 1). Finally a user defined function is also acepted, see examples section for details.


If True (default) add the Bayesian p_value to the legend when kind = t_stat.


Whether or not to plot the mean test statistic. Defaults to True.


How to compute the distributions used as reference for u_values or p_values. Allowed values are “analytical” (default) and “samples”. Use None to do not plot any reference. Defaults to “samples”.

mse :bool

Show scaled mean square error between uniform distribution and marginal p_value distribution. Defaults to False.

n_refint, optional

Number of reference distributions to sample when reference=samples. Defaults to 100.

hdi_prob: float, optional

Probability for the highest density interval for the analytical reference distribution when computing u_values. Should be in the interval (0, 1]. Defaults to 0.94.


Matplotlib color


Number of rows and columns. Defaults to None, the rows and columns are automatically inferred.


Figure size. If None it will be defined automatically.


Text size scaling factor for labels, titles and lines. If None it will be autoscaled based on figsize.


Dictionary containing relations between observed data and posterior/prior predictive data. Dictionary structure:

  • key = data var_name

  • value = posterior/prior predictive var_name

For example, data_pairs = {'y' : 'y_hat'} If None, it will assume that the observed data and the posterior/prior predictive data have the same variable name.

labellerlabeller instance, optional

Class providing the method make_pp_label to generate the labels in the plot titles. Read the Label guide for more details and usage examples.

var_nameslist of variable names

Variables to be plotted, if None all variable are plotted. 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. A la pandas.filter.


Dictionary mapping dimensions to selected coordinates to be plotted. Dimensions without a mapping specified will include all coordinates for that dimension. Defaults to including all coordinates for all dimensions if None.


List of dimensions to flatten in observed_data. Only flattens across the coordinates specified in the coords argument. Defaults to flattening all of the dimensions.


List of dimensions to flatten in posterior_predictive/prior_predictive. Only flattens across the coordinates specified in the coords argument. Defaults to flattening all of the dimensions. Dimensions should match flatten excluding dimensions for data_pairs parameters. If flatten is defined and flatten_pp is None, then flatten_pp=flatten.


Add legend to figure. By default True.

axnumpy array-like of matplotlib axes or bokeh figures, optional

A 2D array of locations into which to plot the densities. If not supplied, Arviz will create its own array of plot areas (and return it).

backendstr, optional

Select plotting backend {“matplotlib”,”bokeh”}. Default “matplotlib”.

plot_ref_kwargsdict, optional

Extra keyword arguments to control how reference is represented. Passed to matplotlib.axes.Axes.plot() or matplotlib.axes.Axes.axhspan() (when kind=u_value and reference=analytical).

backend_kwargsbool, optional

These are kwargs specific to the backend being used, passed to matplotlib.pyplot.subplots() or bokeh.plotting.figure(). For additional documentation check the plotting method of the backend.

group{“prior”, “posterior”}, optional

Specifies which InferenceData group should be plotted. Defaults to ‘posterior’. Other value can be ‘prior’.

showbool, optional

Call backend show function.

axes: matplotlib axes or bokeh figures

See also


Plot for posterior/prior predictive checks.


Plot Leave-One-Out probability integral transformation (PIT) predictive checks.


Plot to compare fitted and unfitted distributions.



Plot Bayesian p_values.

>>> import arviz as az
>>> data = az.load_arviz_data("regression1d")
>>> az.plot_bpv(data, kind="p_value")

Plot custom test statistic comparison.

>>> import arviz as az
>>> data = az.load_arviz_data("regression1d")
>>> az.plot_bpv(data, kind="t_stat", t_stat=lambda x:np.percentile(x, q=50, axis=-1))