DIC: Deviance Information Criterion
Description
Computation of the DIC for an extreme value mixture model
Usage
DIC(x, ...)# S3 method for evmm
DIC(x, ...)
Value
The DIC of a model estimated with extrememix
Arguments
- x
the output of a model estimated with extrememix
- ...
additional arguments for compatibility.
Details
Let \(y\) denote a dataset and \(p(y|\theta)\) the likelihood of a parametric model with parameter \(\theta\). The deviance is defined as \(D(\theta)= -2\log p(y|\theta)\). The deviance information criterion (DIC) is defined as $$DIC = D(\hat\theta) + 2p_D,$$ where \(\hat\theta\) is the posterior estimate of \(\theta\) and \(p_D\) is referred to as the effective number of parameters and defined as $$E_{\theta|y}(D(\theta)) - D(\hat\theta).$$ Models with a smaller DIC are favored.
References
Spiegelhalter, David J., et al. "Bayesian measures of model complexity and fit." Journal of the Royal Statistical Society: Series B 64.4 (2002): 583-639.