A bayesian lower bound for parameter estimation of Poisson data including multiple changes

Lucien Bacharach (1) , Mohammed Nabil El Korso (2) , Alexandre Renaux (1) , Jean-Yves Tourneret (3, 4)

1 L2S - Laboratoire des signaux et systèmes
2 LEME - Laboratoire Energétique Mécanique Electromagnétisme
3 IRIT-MINDS - CoMputational imagINg anD viSion
4 Toulouse INP - Institut National Polytechnique (Toulouse)

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 Cramér-Rao/Weiss-Weinstein bound for which we derive closed-form expressions and illustrate its tightness by numerical simulations.

Keywords: change-point; Weiss-Weinstein bound; Bayesian Cramér-Rao bound; Poisson time series

Domains: Signal and Image Processing

Lucien Bacharach, Mohammed Nabil El Korso, Alexandre Renaux, Jean-Yves Tourneret. A bayesian lower bound for parameter estimation of Poisson data including multiple changes. The 42nd IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2017), Mar 2017, New Orleans, United States. ⟨10.1109/icassp.2017.7953005⟩. ⟨hal-01525499⟩