threshold value, or plot
observation indexes vs $k$ estimates.
pareto_k_table(x)
pareto_k_ids(x, threshold = 0.5)
"plot"(x, ..., label_points = FALSE)plot method, if label_points is
TRUE the observation numbers corresponding to any values of $k$
greater than 0.5 will be displayed in the plot. Any arguments specified in
... will be passed to text and can be used
to control the appearance of the labels.pareto_k_table returns an object of class
"pareto_k_table", which is a matrix with columns "Count" and
"Proportion" and has its own print method.pareto_k_ids returns an integer vector indicating which
observations have Pareto $k$ estimates above threshold.The plot method is called for its side effect and does not
return anything. If x is the result of a call to loo,
plot(x) produces a plot of the estimates of the Pareto shape
parameter $k$. There is no plot method for objects generated by
a call to waic.
loo-package for background on the PSIS
procedure. Here we focus on the interpretation of $k$:
If the estimated tail shape parameter $k$ exceeds $0.5$, the user should be warned, although in practice we have observed good performance for values of $k$ up to 0.7. Even if the PSIS estimate has a finite variance, the user should consider sampling directly from $p(\theta^s | y_{-i})$ for the problematic $i$, use $k$-fold cross-validation, or use a more robust model. Importance sampling is likely to work less well if the marginal posterior $p(\theta^s | y)$ and LOO posterior $p(\theta^s | y_{-i})$ are much different, which is more likely to happen with a non-robust model and highly influential observations. A robust model may reduce the sensitivity to highly influential observations.
Vehtari, A., Gelman, A., and Gabry, J. (2016b). Pareto smoothed importance sampling. arXiv preprint: http://arxiv.org/abs/1507.02646/
loo-package.