A Bayesian Lower Bound for Parameter Estimation of Poisson Data Including Multiple Changes (extended)

TL;DR

This paper develops a Bayesian lower bound for estimating parameters of Poisson data with multiple abrupt changes, accounting for unknown change points and distribution parameters, and demonstrates its effectiveness through simulations.

Contribution

It introduces a mixed Cramer-Rao/Weiss-Weinstein bound for Poisson data with multiple changes, providing closed-form expressions and validation.

Findings

The bound is tight as shown by numerical simulations.

It effectively accounts for both change points and distribution parameters.

The approach improves understanding of estimation limits in complex Poisson models.

Abstract

This paper derives lower bounds for the mean square errors of parameter estimators in the case of Poisson distributed data subjected to multiple abrupt changes. Since both change locations (discrete parameters) and parameters of the Poisson distribution (continuous parameters) are unknown, it is appropriate to consider a mixed Cramer-Rao/Weiss-Weinstein bound for which we derive closed-form expressions and illustrate its tightness by numerical simulations.