WAIC {RprobitB}R Documentation

Compute WAIC value

Description

This function computes the WAIC value of an RprobitB_fit object.

Usage

WAIC(x)

Arguments

x

An object of class RprobitB_fit.

Details

WAIC is short for Widely Applicable (or Watanabe-Akaike) Information Criterion. As for AIC and BIC, the smaller the WAIC value the better the model. Its definition is

WAIC = -2 \cdot lppd + 2 \cdot p_{WAIC},

where lppd stands for log pointwise predictive density and p_{WAIC} is a penalty term proportional to the variance in the posterior distribution that is sometimes called effective number of parameters. The lppd is approximated as follows. Let

p_{is} = \Pr(y_i\mid \theta_s)

be the probability of observation y_i given the sth set \theta_s of parameter samples from the posterior. Then

lppd = \sum_i \log S^{-1} \sum_s p_{si}.

The penalty term is computed as the sum over the variances in log-probability for each observation:

p_{WAIC} = \sum_i V_{\theta} \left[ \log p_{si} \right].

Value

A numeric, the WAIC value, with the following attributes:


[Package RprobitB version 1.1.4 Index]