Spatial Model Analysis Of Spatio-temporal Counting Data And Its Application To Tornado Occurrences

The data types studied in this paper are counting data with temporal and spatial attributes,taking the annual frequency of tornadoes from 1967-2016 in the United States and 2004-2015 in China as examples.Firstly,the spatial correlation analysis is carried out on the annual frequency of tornadoes.The data show that the spatial correlation will be affected by the terrain and not completely inversely proportional to the spatial distance.The Moran's I index,which measures the global autocorrelation,indicates that the occurrence of tornadoes has the characteristics of non-negligible aggregation and dispersion.Secondly,taking the annual frequency of tornadoes under grid division in the United States as an example,under the premise of considering the spatial correlation and over-discrete characteristics of the data,with the aid of hierarchical Bayesian theory,it is assumed that the distribution of the annual frequency of tornadoes in different grids is Poisson distribution,negative binomial distribution or Polya distribution,and the parameters of the distribution are assumed to be random.in order to consider all aspects of uncertainty and spatial correlation characteristics,the Bayesian hierarchical model is established,and the posterior parameters are estimated by MCMC method.Comparing the posterior parameters and the simulation results with the actual data,the results show that the posterior parameters still retain the spatial correlation,and the simulation data show a space similar to the actual variables.The inter-distribution features show that the Bayesian hierarchical model is effective on the premise of considering spatial correlation features and over-discrete features,and the negative binomial distribution has the best performance,which proves that it is more suitable for discrete data with over-discrete features.Finally,the relevant properties of the INAR(1)model of the first-order integral-valued self-regression model,INAR(1),are described and proved.Several different INAR(1)models are assumed for univariate independent bivariate and correlated bivariate data taking non-negative integer data respectively and are simulated and analyzed.The conditional maximum likelihood method and Newton iteration method are used for parameter estimation and optimization.In the related bivariate INAR(1)model,it is assumed that the innovation term follows a two-dimensional discrete distribution.It is assumed that innovation follows a discrete distribution and the parameters of innovation follow multivariate normal distribution.The covariance matrix of normal distribution is a function of spatial distance to consider the spatial correlation characteristics of the data.The simulation analysis shows that the parameter estimation converges and the simulation results are good.,the model hypothesis is reasonable.