Skew Gaussian Markov Random Fields Under Decomposable Graphs

Abstract

Conditional independence and sparsity are pivotal concepts in parsimonious statistical models such as Markov random fields. Statistical modeling in this subject has been limited to the Gaussianity assumption so far, partly due to the difficulty in preserving the Markov property. As the data often exhibit non-normality, we applied a multivariate closed skew normal distribution to introduce a novel skew Gaussian Markov random field with respect to a decomposable graph. Subsequently, after investigating the main probabilistic features of the introduced random process, we specifically focused on modeling autocorrelated data online, and thereafter, an intrinsic version of the skew Gaussian Markov random field was presented. We applied Markov chain Monte Carlo algorithms for Bayesian inference. The identifiability of the parameters was investigated using a simulation study. Finally, the usefulness of our methodology was demonstrated by analyzing two datasets.