WAIC function

Compute WAIC value

This function computes the WAIC value of an RprobitB_fit object.

WAIC(x)

Arguments

• x: An object of class RprobitB_fit.

Returns

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 of p_waic,
• p_si, the output of compute_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

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

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

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