Inference and State Estimation for Stochastic Point Processes.

Abstract

Abstract : Stochastic point processes are models of points distributed randomly in some space; these points may represent, for example, locations (or even trajectories) of tracked objects, times and amounts of precipitation events, or failure times and modes of a complex system. This research project is directed toward two principal problems arising in applications of point processes: statistical inference for point processes whose probability law is unknown entirely or in part, and state estimation for partially observed point processes, i.e., minimum mean squared error reconstruction, realization-by-realization, of random variables that are not directly observable. These problems are examined in several (not disjoint) contexts: stationary point processes, Cox processes, multiplicative intensity processes and Poisson processes. Another thrust of the research is inference for stochastic processes based on point process samples, with the particular goal to investigate inference and state estimation for random fields given point process samples. This report documents results in the research for this period. Additional keywords: Markov processes. (Author)