Robustness of decentralized tests with ϵ-contamination prior

We consider a decentralized detection problem where the prior density is not completely known, but is assumed to belong to an ε-contamination class. The expressions for the infimum and the supremum of the posterior probability that the parameter under question is in a given region, as the prior varies over the ε-contamination class, are derived. Numerical results are obtained for a specific case of an exponentially distributed observation and an exponentially distributed nominal prior. Asymptotic (as number of sensors tends to a large value) results are also obtained. The results illustrate the degree of robustness achieved with quantized observations as compared to unquantized observations