Theory of imprecise sets: imprecise randomness and Bayesian statistics

Abstract

If the realizations of a random variable are imprecise in the sense that two independent laws of randomness can define the presence level of values of the variable in a given interval, we would have to deal with the matters using the idea of imprecise randomness. In Bayesian methodology, inferences are made with reference to a probability law which is followed by a parameter that describes a probability law which is followed by a probabilistic variable. In this article, the mathematics of imprecise randomness has been introduced, and an attempt has been made to link the concept of imprecise randomness with that of Bayesian statistical inference.