Bayesian Assessment of a Skew Spatial Regression Model Based on a Flexible Closed Skew-Normal Random Field using the Hamiltonian Monte Carlo Algorithm

Hosseini, Fatemeh; Karimi, Omid

doi:10.22034/jr_iss.2024.728280

Bayesian Assessment of a Skew Spatial Regression Model Based on a Flexible Closed Skew-Normal Random Field using the Hamiltonian Monte Carlo Algorithm

Document Type : Original Article

Authors

Fatemeh Hosseini ¹

Omid Karimi ²

¹ Semnan University

² Department of Statistics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan

10.22034/jr_iss.2024.728280

Abstract

In practice, spatial data distributions are skewed, which, due to their inherent complexities, poses serious challenges to statistical modeling. Skew-Gaussian random field models offer a flexible framework for analyzing such data; however, many of these models suffer from computational complexity and parameter identifiability issues, which can reduce the accuracy of statistical inference.

In this paper, we develop a spatial regression model based on the flexible closed skew-normal distribution. This model benefits from key properties such as full identifiability, closure under marginalization and conditioning, and high flexibility in capturing complex spatial structures. Bayesian inference is performed using the Hamiltonian Monte Carlo algorithm, a modern Markov Chain Monte Carlo method that leverages gradient information from the target distribution to improve acceptance rate and convergence speed.

To assess the performance of the proposed model, a simulation study is conducted, comparing the HMC-based estimates with those obtained from classical MCMC methods. The results indicate improved accuracy and computational efficiency for the proposed approach. Moreover, the model demonstrates strong capability in analyzing high-dimensional spatial data.

Keywords

Closed Skew Normal Distribution

Identifiability

Spatial Empirical Variogram

Hamiltonian Monte Carlo method