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 |
... |
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
Examples
WAIC(rainfall_ggpd)