Possibilistic analysis of bayesian estimators when imprecise prior information is described by shadowed sets

Abstract

This paper deals with the problem of the analysis of results of Bayesian estimation when the prior information about possible values of estimated parameters is imprecise. We assume that this imprecision is described by the shadowed sets introduced by Pedrycz. The usage of shadowed sets dramatically simplifies all required computations, in comparison, e.g., to the case when it is described by fuzzy sets. A possibilistic methodology for the evaluation of such estimators is proposed. A practical cases of the estimation of reliability characteristics for the exponential distribution is considered.