# arviz.plot_khat#

arviz.plot_khat(khats, color='C0', xlabels=False, show_hlines=False, show_bins=False, bin_format='{1:.1f}%', annotate=False, threshold=None, hover_label=False, hover_format='{1}', figsize=None, textsize=None, coords=None, legend=False, markersize=None, ax=None, hlines_kwargs=None, backend=None, backend_kwargs=None, show=None, **kwargs)[source]#

Plot Pareto tail indices for diagnosing convergence.

Parameters
khatsELPDData containing Pareto shapes information or array of

Pareto tail indices.

colorstr or array_like, optional

Colors of the scatter plot, if color is a str all dots will have the same color, if it is the size of the observations, each dot will have the specified color, otherwise, it will be interpreted as a list of the dims to be used for the color code. If Matplotlib c argument is passed, it will override the color argument

xlabelsbool, optional

Use coords as xticklabels

show_hlinesbool, optional

Show the horizontal lines, by default at the values [0, 0.5, 0.7, 1].

show_binsbool, optional

Show the percentage of khats falling in each bin, as delimited by hlines.

bin_formatstr, optional

The string is used as formatting guide calling bin_format.format(count, pct).

thresholdfloat, optional

Show the labels of k values larger than threshold. Defaults to None, no observations will be highlighted.

hover_labelbool, optional

Show the datapoint label when hovering over it with the mouse. Requires an interactive backend.

hover_formatstr, optional

String used to format the hover label via hover_format.format(idx, coord_label)

figsizetuple, 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 autoscaled based on figsize.

coordsmapping, optional

Coordinates of points to plot. All values are used for computation, but only a a subset can be plotted for convenience.

legendbool, optional

Include a legend to the plot. Only taken into account when color argument is a dim name.

markersize: int, optional

markersize for scatter plot. Defaults to None in which case it will be chosen based on autoscaling for figsize.

ax: axes, optional

Matplotlib axes or bokeh figures.

hlines_kwargs: dictionary, optional

Additional keywords passed to matplotlib.axes.Axes.hlines().

backend: str, optional

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

backend_kwargs: bool, optional

These are kwargs specific to the backend being used, passed to matplotlib.pyplot.subplots() or bokeh.plotting.figure().

showbool, optional

Call backend show function.

kwargs

Additional keywords passed to matplotlib.axes.Axes.scatter().

Returns
axesmatplotlib axes or bokeh figures

psislw

Pareto smoothed importance sampling (PSIS).

Notes

The Generalized Pareto distribution (GPD) may be used to diagnose convergence rates for importance sampling. GPD has parameters offset, scale, and shape. The shape parameter is usually denoted with k. k also tells how many finite moments the distribution has. The pre-asymptotic convergence rate of importance sampling can be estimated based on the fractional number of finite moments of the importance ratio distribution. GPD is fitted to the largest importance ratios and the estimated shape parameter k, i.e., \hat{k} can then be used as a diagnostic (most importantly if \hat{k} > 0.7, then the convergence rate is impractically low). See [1].

References

1

Vehtari, A., Simpson, D., Gelman, A., Yao, Y., Gabry, J.,

1. Pareto Smoothed Importance Sampling. arXiv:1507.02646 [stat].

Examples

Plot estimated pareto shape parameters showing how many fall in each category.

>>> import arviz as az


Show xlabels

>>> centered_eight = az.load_arviz_data("centered_eight")
>>> khats = az.loo(centered_eight, pointwise=True).pareto_k
>>> az.plot_khat(khats, xlabels=True, threshold=1)


Use custom color scheme

>>> counties = radon.posterior.County[radon.constant_data.county_idx].values
>>> colors = [
...     "blue" if county[-1] in ("A", "N") else "green" for county in counties
... ]