Estimation of high order simultaneous equations spatial autoregressive model: An efficient Bayesian approach

We consider the Bayesian estimation of high order simultaneous equations spatial autoregressive model for large scale spatial data sets, which tackles the computational difficulty of the constrained optimization problem over multiple spatial parameters from different outcome equations in the traditional likelihood-based method. We further propose an efficient Markov Chain Monte Carlo (MCMC) algorithm utilizing the exchange algorithm to address the computational challenges associated with evaluating the Jacobian determinant with a large number of parameters under a large sample size. Monte Carlo experiments demonstrate our proposed Bayesian methods exhibit good performance in finite samples, and the exchange algorithm manages to reduce computation time by approximately two-thirds compared to a typical Bayesian MCMC method.