WAIC {extrememix}R Documentation

Widely Applicable Information Criteria

Description

Computation of the WAIC for an extreme value mixture model.

Usage

WAIC(x, ...)

## S3 method for class 'evmm'
WAIC(x, ...)

Arguments

x

the output of a model estimated with extrememix.

...

additional arguments for compatibility.

Details

Consider a dataset y=(y_1,\dots,y_n), p(y|\theta) the likelihood of a parametric model with parameter \theta, and (\theta^{(1)},\dots,\theta^{(S)}) a sample from the posterior distribution p(\theta|y). Define

\textnormal{llpd} = \sum_{i=1}^n \log\left(\sum_{i=1}^Sp(y_i|\theta^{(s)}\right)

and

p_\textnormal{WAIC} = \sum_{i=1}^n Var_{\theta|y}(\log p(y_i|\theta)).

Then the Widely Applicable Information Criteria is defined as

WAIC = -2\textnormal{llpd} + 2p_\textnormal{WAIC}.

Models with a smaller WAIC are favored.

Value

The WAIC of a model estimated with extrememix

References

Gelman, Andrew, Jessica Hwang, and Aki Vehtari. "Understanding predictive information criteria for Bayesian models." Statistics and computing 24.6 (2014): 997-1016.

Watanabe, Sumio. "A widely applicable Bayesian information criterion." Journal of Machine Learning Research 14.Mar (2013): 867-897.

See Also

DIC

Examples

WAIC(rainfall_ggpd)


[Package extrememix version 0.0.1 Index]