Bayesian estimation analysis of partially linear varying coefficient skew-normal spatial autoregression models

This paper presents a novel partially linear varying coefficient skew-normal spatial autoregression model for accommodating actual data that exhibit skewed tail behaviour, which may not be well modelled by normally distributed errors. We first utilize Bayesian P-splines to effectively approximate the nonparametric components of the model. Along with the Metropolis importance sampling algorithm for the nonparametric components of the model, we propose an effective Markov Chain Monte Carlo algorithm that integrates Gibbs sampling and the Metropolis-Hastings algorithm to generate posterior samples from the joint posterior distribution, thus facilitating statistical inference. We carry out extensive simulation studies to investigate the finite sample performance of the proposed method. Numerical results show that the proposed method is capable of effectively addressing the characteristics of skewed data and yielding conclusions that align well with the simulations under consideration. Finally, a real-data application is provided for illustrative purposes.