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Weiss-Weinstein bound for change-point estimation

We compute the Weiss-Weinstein bound in the context of change-point estimation in a multivariate time series whatever the considered distribution of the data as well the prior. Closed-form expressions are then given in the case of Gaussian observations with change of mean and variance and in the case of parameter change in a Poisson distribution. The proposed bound is shown to be tighter than the previous bounds which were originally derived in the deterministic context and provides a better approximation of the maximum a posteriori estimator global mean square error.