Statistical Inference Based on the Possibility and Belief Measures

In statistical inference, we infer the population parameter based on the realization of sample statistics. This can be considered in the framework of inductive inference. We show, in Chen (1993), that if we measure a parameter by the possibility (or belief) measure, we can have an inductive inference similar to the Bayesian inference in belief update. In this article we apply this inference to statistical estimation and hypotheses evaluation (testing) for some parametric models, and compare them to the classical statistical inferences for both one-sample and two-sample problems.