Finite-Length Bounds on Hypothesis Testing Subject to Vanishing Type I Error Restrictions

Sequential Multiple Hypothesis Testing with Type I Error Control

This work studies multiple hypothesis testing in the setting when we obtain data sequentially and may choose when to stop sampling. We summarize the notion of a sequential pvalue (one that can be continually updated and still maintain a type I error guarantee) and provide several examples from the literature. This tool allows us to convert fixedhorizon step-up or step-down multiple hypothesis t...

Statistical Hypothesis Testing and Lower Bounds to the Error Probability

Two alternative exact characterizations of the minimum error probability of Bayesian M -ary hypothesis testing are derived. The first expression corresponds to the error probability of an induced binary hypothesis test and implies the tightness of the meta-converse bound by Polyanskiy, Poor and Verdú; the second expression is function of an information-spectrum measure and implies the tightness...

On the Subject of Hypothesis Testing

In this paper, the definition of a statistical hypothesis is discussed, and the considerations which need to be addressed when testing a hypothesis. In particular, the p-value, significance level, and power of a test are reviewed. Finally, the often quoted confidence interval is given a brief introduction.

Mismatched Decoding: Finite-Length Bounds, Error Exponents and Approximations

This paper considers the problem of channel coding with a given (possibly suboptimal) decoding rule. Finite-length upper and lower bounds on the random-coding error probability for a general codeword distribution are given. These bounds are applied to three random-coding ensembles: i.i.d., constant-composition, and cost-constrained. Ensembletight error exponents are presented for each ensemble,...

Hypothesis Testing for Arbitrary Bounds