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 \(\hat{k}\) for diagnosing convergence in PSIS-LOO.

khatsELPDData or array_like

The input Pareto tail indices to be plotted. It can be an ELPDData object containing Pareto shapes or an array. In this second case, all the values in the array are interpreted as Pareto tail indices.

colorstr or array_like, default “C0”

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, default False

Use coords as xticklabels.

show_hlinesbool, default False

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

show_binsbool, default False

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. If None (default), no observations will be highlighted.

hover_labelbool, default False

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

hover_formatstr, default “{1}”

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

figsize(float, float), optional

Figure size. If None it will be defined automatically.

textsizefloat, 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. See this section for usage examples.

legendbool, default False

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

markersizeint, optional

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

axaxes, optional

Matplotlib axes or bokeh figures.

hlines_kwargsdict, optional

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

backend{“matplotlib”, “bokeh”}, default “matplotlib”

Select plotting backend.

backend_kwargsdict, 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.

showbool, optional

Call backend show function.


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

axesmatplotlib Axes or bokeh_figures

See also


Pareto smoothed importance sampling (PSIS).


The Generalized Pareto distribution (GPD) diagnoses convergence rates for importance sampling. GPD has parameters offset, scale, and shape. The shape parameter (\(k\)) tells the distribution’s number of finite moments. 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 interprets 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].



Vehtari, A., Simpson, D., Gelman, A., Yao, Y., Gabry, J. (2024). Pareto Smoothed Importance Sampling. Journal of Machine Learning Research, 25(72):1-58.


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

>>> import arviz as az
>>> radon = az.load_arviz_data("radon")
>>> loo_radon = az.loo(radon, pointwise=True)
>>> az.plot_khat(loo_radon, show_bins=True)

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
... ]
>>> az.plot_khat(loo_radon, color=colors)