dic.samples: Generate penalized deviance samples In rjags: Bayesian Graphical Models using MCMC

 dic.samples R Documentation

Generate penalized deviance samples

Description

Function to extract random samples of the penalized deviance from a `jags` model.

Usage

``````dic.samples(model, n.iter, thin = 1, type, ...)
``````

Arguments

 `model` a jags model object `n.iter` number of iterations to monitor `thin` thinning interval for monitors `type` type of penalty to use `...` optional arguments passed to the update method for jags model objects

Details

The `dic.samples` function generates penalized deviance statistics for use in model comparison. The two alternative penalized deviance statistics generated by `dic.samples` are the deviance information criterion (DIC) and the penalized expected deviance. These are chosen by giving the values “pD” and “popt” respectively as the `type` argument.

DIC (Spiegelhalter et al 2002) is calculated by adding the “effective number of parameters” (`pD`) to the expected deviance. The definition of `pD` used by `dic.samples` is the one proposed by Plummer (2002) and requires two or more parallel chains in the model.

DIC is an approximation to the penalized plug-in deviance, which is used when only a point estimate of the parameters is of interest. The DIC approximation only holds asymptotically when the effective number of parameters is much smaller than the sample size, and the model parameters have a normal posterior distribution.

The penalized expected deviance (Plummer 2008) is calculated by adding the optimism (`popt`) to the expected deviance. The `popt` penalty is at least twice the size of the `pD` penalty, and penalizes complex models more severely.

Value

An object of class “dic”. This is a list containing the following elements:

 `deviance` A numeric vector, with one element for each observed stochastic node, containing the mean deviance for that node `penalty` A numeric vector, with one element for each observed stochastic node, containing an estimate of the contribution towards the penalty `type` A string identifying the type of penalty: “pD” or “popt”

Note

The `popt` penalty is estimated by importance weighting, and may be numerically unstable.

Martyn Plummer

References

Spiegelhalter, D., N. Best, B. Carlin, and A. van der Linde (2002), Bayesian measures of model complexity and fit (with discussion). Journal of the Royal Statistical Society Series B 64, 583-639.

Plummer, M. (2002), Discussion of the paper by Spiegelhalter et al. Journal of the Royal Statistical Society Series B 64, 620.

Plummer, M. (2008) Penalized loss functions for Bayesian model comparison. Biostatistics doi: 10.1093/biostatistics/kxm049

`diffdic`