Multiresolution Intensity Estimation of Piecewise Linear Poisson Processes

Abstract

Given observations of a one-dimensional piecewise linear, length-M Poisson intensity function, our goal is to estimate both the partition points and the parameters of each segment. In order to determine where the breaks lie, we develop a maximum penalized likelihood estimator based on information-theoretic complexity penalization. We construct a probabilistic model of the observations within a multiscale framework, and use this framework to devise a computationally efficient optimization algorithm, based on a tree-pruning approach, to compute the MPLE.