waic.angmcmc: Watanabe-Akaike Information Criterion (WAIC) for angmcmc...

In BAMBI: Bivariate Angular Mixture Models

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, int.displ specifies integer displacement in wnorm and wnorm2 models. See fit_wnormmix and fit_wnorm2mix for more details.

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)

BAMBI documentation built on March 31, 2023, 11:24 p.m.