DIC {BAMBI} | R Documentation |
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 |
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)