Comparison between the Bayesian method and the Particle Swarm Algorithm for Estimating a Spatial Autoregressive Model

The spatial autoregressive model is one of the models that is very similar to ordinary time series models, as the spatial mixed model is formed when the spatially lagged dependent variable is included as one of the explanatory variables. To find out whether or not there is spatial dependence between these variables, a spatial autoregressive model is used Moran Test. If this reliability is ignored or not taken into consideration, this leads to the loss of important information. Accordingly, in the research, the spatial autoregressive model was estimated when the model error is distributed with a mixed distribution (represented by the t-distribution) by the Bayesian method when the initial information is available from one side of the artificial intelligence algorithm, represented by the Particle Swarm Optimization (PSO) algorithm from On the other hand, the application to real data related to the poverty gap sample in developing countries for the years (2005-2010-2015-2020) and through the Moran test and the Lagrange multiplier showed that there is a spatial autocorrelation between the observations and the researchers concluded that the subsequent probability distribution of the vector of parameters (▁θ) follows a multivariate t distribution, and the posterior probability distribution of the variance parameter was an uncommon but appropriate distribution (Proper), in addition to the superiority of the PSO algorithm for estimating the spatial autoregressive model with heavy tails in the Bayesian manner through the criteria of mean square error and mean relative error.