Arimoto–Rényi Conditional Entropy and Bayesian $M$ -Ary Hypothesis Testing

Arimoto-Rényi conditional entropy and Bayesian hypothesis testing

This paper gives upper and lower bounds on the minimum error probability of Bayesian M -ary hypothesis testing in terms of the Arimoto-Rényi conditional entropy of an arbitrary order α. The improved tightness of these bounds over their specialized versions with the Shannon conditional entropy (α = 1) is demonstrated. In particular, in the case where M is finite, we show how to generalize Fano’s...

Distributed M-ary hypothesis testing with binary local decisions

Parallel distributed detection schemes for M-ary hypothesis testing often assume that for each observation the local detector transmits at least log2 M bits to a data fusion center (DFC). However, it is possible for less than log2 M bits to be available, and in this study we consider 1-bit local detectors with M > 2. We develop conditions for asymptotic detection of the correct hypothesis by th...

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...

Tsallis Entropy and Conditional Tsallis Entropy of Fuzzy Partitions

The purpose of this study is to define the concepts of Tsallis entropy and conditional Tsallis entropy of fuzzy partitions and to obtain some results concerning this kind entropy. We show that the Tsallis entropy of fuzzy partitions has the subadditivity and concavity properties. We study this information measure under the refinement and zero mode subset relations. We check the chain rules for ...

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