| waic.angmcmc {BAMBI} | R Documentation |
Watanabe-Akaike Information Criterion (WAIC) for angmcmc objects
Description
Watanabe-Akaike Information Criterion (WAIC) for angmcmc objects
Usage
## S3 method for class 'angmcmc'
waic(x, ...)
Arguments
x |
angmcmc object. |
... |
additional model specific arguments to be passed to waic from loo. For example, |
Details
Given a deviance function D(\eta) = -2 \log(p(y|\eta)), and an estimate
\eta* = (\sum \eta_i) / n of the posterior mean
E(\eta|y), where y = (y_1, ..., y_n) denote the data, \eta is the unknown
parameter vector of the model, \eta_1, ..., \eta_N are MCMC samples from the posterior
distribution of \eta given y and p(y|\eta) is the likelihood function,
the Watanabe-Akaike Information Criterion (WAIC) is defined as
WAIC = LPPD - p_W
where
LPPD = \sum_{i=1}^n \log (N^{-1} \sum_{s=1}^N p(y_i|\eta_s) )
and (form 1 of)
p_W = 2 \sum_{i=1}^n [ \log (N^{-1} \sum_{s=1}^N p(y_i|\eta_s) ) - N^{-1} \sum_{s=1}^N \log \:p(y_i|\eta_s) ].
An alternative form (form 2) for p_W is given by
p_W = \sum_{i=1}^n \hat{var} \log p(y_i|\eta)
where for i = 1, ..., n, \hat{var} \log p(y_i|\eta) denotes the estimated variance
of \log p(y_i|\eta) based on the realizations \eta_1, ..., \eta_N.
Note that waic.angmcmc calls waic for computation. If the likelihood contribution of each data
point for each MCMC iteration is available in object (can be returned by setting return_llik_contri = TRUE)
during fit_angmix call), waic.array is used; otherwise waic.function is
called. Computation is much faster if the likelihood contributions are available - however, they are very
memory intensive, and by default not returned in fit_angmix.
Value
Computes the WAIC for a given angmcmc object.
Examples
# illustration only - more iterations needed for convergence
fit.vmsin.20 <- fit_vmsinmix(tim8, ncomp = 3, n.iter = 20,
n.chains = 1, return_llik_contri = TRUE)
library(loo)
waic(fit.vmsin.20)