Bayesian Nonparametric Nonhomogeneous Poisson Process with Applications to USGS Earthquake Data

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 estimate of the intensity of spatial point patterns in different areas while considering heterogeneity. An efficient Markov chain Monte Carlo (MCMC) algorithm is proposed for our method. 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.