Hidden Markov Model In Spatial Statistics

Spatial statistics is the issue of space statistically another discipline, it is a rapid development of Applied Mathematics branch. It originated in the early 1950s to help the mining industry in terms of deposits. With computer in 1970s and the popularity of the substantial increase in computational speed, spatial statistical analysis techniques gradually extended to other areas of earth science. Now commonly found in the need to address the time or space-related data in the field of science and technology, and its main applications include remote sensing, land and resources estimates, agriculture and forestry, oceanography, epidemiology, ecology and environmental observation.In this paper, we present methodology to extend hidden Markov models to the spatial field, and use this class of models to analyze spatial heterogeneity of count data on a rare phenomenon. This situation occurs commonly in many domains of application, particularly in disease mapping. We assume that the counts follow a Poisson model at the lowest level of the hierarchy, and introduce a finite-mixture model for the Poisson rates at the next level. The novelty lies in the model for allocation to the mixture components, which follows a spatially correlated process, the Potts model, and in treating the number of components of the spatial mixture as unknown. Inference is performed in a Bayesian framework using reversible jump Markov chain Monte Carlo. Finally, we applie the model to the epidemiology field.The whole text is divided into four chapters. The first chapter is devoted to the status of the space statistics, this study also indicates that the practical value, but also gives a brief review of spatial statistics.Chapter II through the introduction of the concept of Markov process, the data is extended to the spatial structure hidden Markov random field for the space behind the statistical theory of preparing the necessary conditions. Chapter III on Markov chain Monte Carlo methods, then we deduce Potts mixture model using a sample of four different movements, and proceed to the realization of BYM model.Chapter IV discusses the model simulation, contrast and applications, and revealed by the study of this model and work at home and abroad have been linked. At the same time, the subject is given on the direction of development.