Detecting influential observations in spatial models using Bregman divergence

Abstract

How to evaluate if a spatial model is well ajusted to a problem? How to know if it is the best model between the class of conditional autoregressive (CAR) and simultaneous autoregressive (SAR) models, including homoscedasticity and heteroscedasticity cases? To answer these questions inside Bayesian framework, we propose new ways to apply Bregman divergence, as well as recent information criteria as widely applicable information criterion (WAIC) and leave-one-out cross-validation (LOO).

The functional Bregman divergence is a generalized form of the well known Kullback-Leiber (KL) divergence. There is many special cases of it which might be used to identify influential points. All the posterior distributions displayed in this text were estimate by Hamiltonian Monte Carlo (HMC), a optimized version of Metropolis-Hasting algorithm. All ideas showed here were evaluate by both: simulation and real data.