Bayesian nonparametric nonhomogeneous Poisson process with applications to USGS earthquake data

Abstract

Intensity estimation is a common problem in statistical analysis of spatial point pattern data. This paper proposes a nonparametric Bayesian method for estimating the spatial point process intensity based on mixture of finite mixture (MFM) model. MFM approach leads to a consistent and simultaneous estimate of the intensity surface of spatial point pattern and the clustering information (number of clusters and the clustering configurations) of subareas of the intensity surface. An efficient Markov chain Monte Carlo (MCMC) algorithm is proposed for our method, where it performs a marginalization over the number of clusters which avoids complicated reversible jump MCMC or allocation samplers. Extensive simulation studies are carried out to examine empirical performance of the proposed method. The usage of our proposed method is further illustrated with the analysis of the Earthquake Hazards Program of United States Geological Survey (USGS) earthquake data.