Annual Mean Temperature and Rain Precipitation in North America Using NHPP to Detect Climate Changes

In this study, non-homogeneous Poisson processes (NHPP) are assumed to analyze annual averagetemperatures and rain precipitations, considering climate data for some regions of North America reportedfor a long period. A power law process (PLP) is assumed for the intensity function (derivative of the meanvalue function) or rateλ(t),t≥0of the NHPP which the Poisson events occur considering data (accumulatednumber of years in a given time interval [0,t) where the climate measure is above a threshould given by theoveral average in the assumed period) in presence or not of a change-point. The parameters of the assumedmodel are estimated under a Bayesian approach and using MCMC (Markov Chain Monte Carlo) methods.Alternatively to the use of a PLP process, we also assume a polynomial parametrical form for the mean valuefunction of the NHPP process where a simple Bayesian inference approach is proposed to get better fit for theintensity and mean value functions of the NHPP process. From the fitted models it was possible to to detect theyears where climate changes occurred.