DIC {BAMBI}

Deviance Information Criterion (DIC) for angmcmc objects

Description

Deviance Information Criterion (DIC) for angmcmc objects

Usage

DIC(object, form = 2, ...)

Arguments

object

angular MCMC object.

form

form of DIC to use. Available choices are 1 and 2 (default). See details.

...

additional model specific arguments to be passed to DIC. For example, int.displ specifies integer dispacement in wnorm and wnorm2 models. See fit_wnormmix and fit_wnorm2mix for more details.

Details

Given a deviance function D(\theta) = -2 log(p(y|\theta)), and an estimate \theta* = (\sum \theta_i) / N of the posterior mean E(\theta|y), where y denote the data, \theta are the unknown parameters of the model, \theta_1, ..., \theta_N are MCMC samples from the posterior distribution of \theta given y and p(y|\theta) is the likelihood function, the (form 1 of) Deviance Infomation Criterion (DIC) is defined as

DIC = 2 ( (\sum_{s=1}^N D(\theta_s)) / N - D(\theta*) )

The second form for DIC is given by

DIC = D(\theta*) - 4 \hat{var} \log p(y|\theta_s)

where for i = 1, ..., n, \hat{var} \log p(y|\theta) denotes the estimated variance of the log likelihood based on the realizations \theta_1, ..., \theta_N.

Like AIC and BIC, DIC is an asymptotic approximation for large samples, and is only valid when the posterior distribution is approximately normal.

Value

Computes the DIC 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)
DIC(fit.vmsin.20)