Statistical inference for doubly stochastic multichannel Poisson processes: A PCA approach

Efficient computational algorithms for making inferences about the intensity process of an observed doubly stochastic multichannel Poisson process are designed. The proposed solution is based on a numerical version of principal component analysis (PCA) of stochastic processes and hence it can be applied simply with knowledge of the first- and second-order moments of the intensity process of interest. The technique provided is valid for solving all types of estimation problems: filtering, prediction and smoothing.