Source code for arviz.plots.bfplot

# Plotting and reporting Bayes Factor given idata, var name, prior distribution and reference value
# pylint: disable=unbalanced-tuple-unpacking
import logging

from numpy import interp

from import extract
from .plot_utils import get_plotting_function
from ..stats.density_utils import _kde_linear

_log = logging.getLogger(__name__)

[docs] def plot_bf( idata, var_name, prior=None, ref_val=0, colors=("C0", "C1"), figsize=None, textsize=None, hist_kwargs=None, plot_kwargs=None, ax=None, backend=None, backend_kwargs=None, show=None, ): r"""Approximated Bayes Factor for comparing hypothesis of two nested models. The Bayes factor is estimated by comparing a model (H1) against a model in which the parameter of interest has been restricted to be a point-null (H0). This computation assumes the models are nested and thus H0 is a special case of H1. Notes ----- The bayes Factor is approximated as the Savage-Dickey density ratio algorithm presented in [1]_. Parameters ---------- idata : InferenceData Any object that can be converted to an :class:`arviz.InferenceData` object Refer to documentation of :func:`arviz.convert_to_dataset` for details. var_name : str, optional Name of variable we want to test. prior : numpy.array, optional In case we want to use different prior, for example for sensitivity analysis. ref_val : int, default 0 Point-null for Bayes factor estimation. colors : tuple, default ('C0', 'C1') Tuple of valid Matplotlib colors. First element for the prior, second for the posterior. figsize : (float, float), optional Figure size. If `None` it will be defined automatically. textsize : float, optional Text size scaling factor for labels, titles and lines. If `None` it will be auto scaled based on `figsize`. plot_kwargs : dict, optional Additional keywords passed to :func:`matplotlib.pyplot.plot`. hist_kwargs : dict, optional Additional keywords passed to :func:`arviz.plot_dist`. Only works for discrete variables. ax : axes, optional :class:`matplotlib.axes.Axes` or :class:`bokeh.plotting.Figure`. backend : {"matplotlib", "bokeh"}, default "matplotlib" Select plotting backend. backend_kwargs : dict, optional These are kwargs specific to the backend being used, passed to :func:`matplotlib.pyplot.subplots` or :class:`bokeh.plotting.figure`. For additional documentation check the plotting method of the backend. show : bool, optional Call backend show function. Returns ------- dict : A dictionary with BF10 (Bayes Factor 10 (H1/H0 ratio), and BF01 (H0/H1 ratio). axes : matplotlib_axes or bokeh_figure References ---------- .. [1] Heck, D., 2019. A caveat on the Savage-Dickey density ratio: The case of computing Bayes factors for regression parameters. Examples -------- Moderate evidence indicating that the parameter "a" is different from zero. .. plot:: :context: close-figs >>> import numpy as np >>> import arviz as az >>> idata = az.from_dict(posterior={"a":np.random.normal(1, 0.5, 5000)}, ... prior={"a":np.random.normal(0, 1, 5000)}) >>> az.plot_bf(idata, var_name="a", ref_val=0) """ posterior = extract(idata, var_names=var_name).values if ref_val > posterior.max() or ref_val < posterior.min(): _log.warning( "The reference value is outside of the posterior. " "This translate into infinite support for H1, which is most likely an overstatement." ) if posterior.ndim > 1: _log.warning("Posterior distribution has {posterior.ndim} dimensions") if prior is None: prior = extract(idata, var_names=var_name, group="prior").values if posterior.dtype.kind == "f": posterior_grid, posterior_pdf = _kde_linear(posterior) prior_grid, prior_pdf = _kde_linear(prior) posterior_at_ref_val = interp(ref_val, posterior_grid, posterior_pdf) prior_at_ref_val = interp(ref_val, prior_grid, prior_pdf) elif posterior.dtype.kind == "i": posterior_at_ref_val = (posterior == ref_val).mean() prior_at_ref_val = (prior == ref_val).mean() bf_10 = prior_at_ref_val / posterior_at_ref_val bf_01 = 1 / bf_10 bfplot_kwargs = dict( ax=ax, bf_10=bf_10.item(), bf_01=bf_01.item(), prior=prior, posterior=posterior, ref_val=ref_val, prior_at_ref_val=prior_at_ref_val, posterior_at_ref_val=posterior_at_ref_val, var_name=var_name, colors=colors, figsize=figsize, textsize=textsize, hist_kwargs=hist_kwargs, plot_kwargs=plot_kwargs, backend_kwargs=backend_kwargs, show=show, ) plot = get_plotting_function("plot_bf", "bfplot", backend) axes = plot(**bfplot_kwargs) return {"BF10": bf_10, "BF01": bf_01}, axes