A Hamiltonian Monte Carlo EM algorithm for generalized linear mixed models with spatial skew latent variables

Spatial generalized linear mixed models with skew latent variables are usually used to model discrete spatial responses that have some skewness. Since the likelihood function in these models is complex, the Monte Carlo EM algorithms are commonly applied to estimate the model parameters. In this paper, we use an approximately stationary skew Gaussian random field, which is more flexible than the Gaussian one, to analyze the skew discrete spatial responses. We also present a new hybrid EM algorithm using the Hamiltonian Monte Carlo method, which is both faster and more accurate than the Monte Carlo EM algorithm. The performance of the proposed skew model with a hybrid algorithm is evaluated through a simulation study and an application to the earthquake data of Iran. The simulation results indicate that the proposed Hamiltonian algorithm with the skew random field has better performance than the existing models. In addition, spatial prediction is presented through the proposed approach for the earthquake data on the entire map of Iran, where high-risk areas with the probability of large earthquakes are identified.