This function computes the WAIC value of an RprobitB_fit object.
Value
A numeric, the WAIC value, with the following attributes:
se_waic, the standard error of the WAIC value,lppd, the log pointwise predictive density,p_waic, the effective number of parameters,p_waic_vec, the vector of summands ofp_waic,p_si, the output ofcompute_p_si.
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 \(s\)th 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: $$p_{WAIC} = \sum_i V_{\theta} \left[ \log p_{si} \right].$$