Bayesian Analysis of Spatial Model for Frequency of Tornadoes

Frequency analysis of tornadoes is very important for risk analysis and disaster control. In this paper, the annual frequency of tornadoes that occurred in the United States from 1967 to 2016 is analyzed. The simple analysis shows that frequencies of tornadoes of different sites are spatially correlated and over-dispersed. To explain the two characteristics of the data, the Bayesian hierarchical model is proposed. For comparison purposes, the Bayesian model with negative binomial distribution, Poisson distribution, Polya distribution, and first-order, non-negative, integer-valued autoregressive model with Bell innovations(BL-INAR(1)) are considered to fit the frequency of tornado. The distribution parameters of all sites are assumed to be spatially correlated, and the corresponding Bayesian hierarchical models were established. MCMC (Markov Chain Monte Carlo) method is applied to parameter estimations and relative statistical inference. By comparison of the analysis results, the negative binomial distribution is recommended to analyze the overdispersion and spatial correlation among the sites of the data. The comparison between the simulated frequencies based on the proposed model and the actual frequencies also verifies that the proposed method is a better model for the data.