Posterior Covariance Information Criterion

We introduce an information criterion, PCIC, for predictive evaluation based on quasi-posterior distributions. It is regarded as a natural generalization of widely applicable information criterion (WAIC) and can be computed via a single Markov Chain Monte Carlo run. PCIC is useful in a variety of predictive settings that are not well dealt with in WAIC, including weighted likelihood inference and quasi-Bayesian prediction.