Bayesian Estimation With Imprecise Likelihoods: Random Set Approach

In many practical applications of statistical signal processing, the likelihood functions are only partially known. The measurement model in this case is affected by two sources of uncertainty: stochastic uncertainty and imprecision. Following the framework of random set theory [1], the paper presents the optimal Bayesian estimator for this problem. The resulting Bayes estimator in general has no analytic closed form solution, but can be approximated, for example, using the Monte Carlo method. A numerical example is included to illustrate the theory.