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

Lucien Bacharach; Mohammed Nabil El Korso; Alexandre Renaux; Jean-Yves Tourneret

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

1 L2S - Laboratoire des signaux et systèmes

2 LEME - Laboratoire Energétique Mécanique Electromagnétisme

3 IRIT - Institut de recherche en informatique de Toulouse

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

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

Document type :

Conference papers

Domain :

Computer Science [cs] / Signal and Image Processing

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https://hal-centralesupelec.archives-ouvertes.fr/hal-01525499
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