B1066
Title: Bayesian estimation for some self-exciting point processes
Authors: Tom Stindl - UNSW (Australia) [presenting]
Abstract: Methods of inference for point processes whose conditional intensity depends on unobserved latent indicator variables are generally challenging due to an intractable likelihood. Examples of recently proposed models of this type are the renewal epidemic type aftershock sequence (RETAS) model and the autoregressive moving average (ARMA) point process. Both these processes allow points of different types e.g., background events or excited events, to have different contributions to the conditional intensity. Since the event types are not part of the observed data, a Bayesian treatment of model inference is proposed that includes the latent variables in its formulation. The latent variables represent the genealogical tree that connects the points, as immigrants or direct offspring, due to the models' connection to a branching process. The inference is based on the complete data likelihood which weakens the parameters' dependence when sampling from the posterior. These methods are applied to an earthquake catalog from South California using the RETAS and ARMA point processes. Future seismicity is forecasted in a simulation-based approach which allows parameter uncertainty to be incorporated into the predictions.
