Bayesian Sequential Hypothesis Testing

Multisource Bayesian sequential hypothesis testing

On some probability space (Ω,F,P), let (X)t≥0, 1 ≤ i ≤ d be d independent Brownian motions with constant drifts μ(i), 1 ≤ i ≤ d, and (T (j) n , Z n )n≥1, 1 ≤ j ≤ m be m independent compound Poisson processes independent of the Brownian motions (X)t≥0, 1 ≤ i ≤ d. For every 1 ≤ j ≤ m, (T (j) n )n≥1 are the arrival times, and (Z n )n≥1 are the marks on some measurable space (E, E), with arrival ra...

Multisource Bayesian sequential binary hypothesis testing problem

We consider the problem of testing two simple hypotheses about unknown local characteristics of several independent Brownian motions and compound Poisson processes. All of the processes may be observed simultaneously as long as desired before a final choice between hypotheses is made. The objective is to find a decision rule that identifies the correct hypothesis and strikes the optimal balance...

Bayesian Fuzzy Hypothesis Testing with Imprecise Prior Distribution

This paper considers the testing of fuzzy hypotheses on the basis of a Bayesian approach. For this, using a notion of prior distribution with interval or fuzzy-valued parameters, we extend a concept of posterior probability of a fuzzy hypothesis. Some of its properties are also put into investigation. The feasibility and effectiveness of the proposed methods are also cla...

Active Sequential Hypothesis Testing

Consider a decision maker who is responsible to dynamically collect observations so as to enhance his information about an underlying phenomena of interest in a speedy manner while accounting for the penalty of wrong declaration. Due to the sequential nature of the problem, the decision maker relies on his current information state to adaptively select the most “informative” sensing action amon...

Bayesian Hypothesis Testing 1 Running head: BAYESIAN HYPOTHESIS TESTING The Need for Bayesian Hypothesis Testing in Psychological Science