Spatial count models on the number of unhealthy days in Tehran

Spatial count data is usually found in most sciences such as environmental science, meteorology, geology and medicine. Spatial generalized linear models based on poisson (poisson-lognormal spatial model) and binomial (binomial-logitnormal spatial model) distributions are often used to analyze discrete count data in which spatial correlation is observed. The likelihood function of these models is complex as analytic and so computation.  The Bayesian approach using Monte Carlo Markov chain algorithms can be a solution to fit these models, although there are usually problems with low sample acceptance rates and long runtime to implement the algorithms. An appropriate solution is to use the Hamilton (hybrid) Monte Carlo algorithm  in The Bayesian approach. In this paper, the new Hamilton (hybrid) Monte Carlo method for Bayesian analysis of spatial count models on air pollution data in Tehran is studied. Also, the two common Monte Carlo algorithms such as the Markov chain (Gibbs and Metropolis-Hastings) and Langevin-Hastings are used to apply  the complete Bayesian approach on the data modeling.  Finally, an appropriate approach to data analysis and forecasting in all points of the city is introduced with the diagnostic criteria.