Use of non-homogeneous Poisson process (NHPP) in presence of change-points to analyze drought periods: a case study in Brazil

Rain precipitation in the last years has been very atypical in different regions of the world, possibly, due to climate changes. We analyze Standard Precipitation Index (SPI) measures (1, 3, 6 and 12-month timescales) for a large city in Brazil: Campinas located in the southeast region of Brazil, São Paulo State, ranging from January 01, 1947 to May 01, 2011. A Bayesian analysis of non-homogeneous Poisson processes in presence or not of change-points is developed using Markov Chain Monte Carlo methods in the data analysis. We consider a special class of models: the power law process. We also discuss some discrimination methods for the choice of the better model to be used for the rain precipitation data.