Related papers: Finite-Length Bounds on Hypothesis Testing Subject…
A distributed binary hypothesis testing problem, in which multiple observers transmit their observations to a detector over noisy channels, is studied. Given its own side information, the goal of the detector is to decide between two…
Identification of latent binary sequences from a pool of noisy observations has a wide range of applications in both statistical learning and population genetics. Each observed sequence is the result of passing one of the latent…
Bounding the best achievable error probability for binary classification problems is relevant to many applications including machine learning, signal processing, and information theory. Many bounds on the Bayes binary classification error…
Quantum hypothesis testing (QHT) has been traditionally studied from the information-theoretic perspective, wherein one is interested in the optimal decay rate of error probabilities as a function of the number of samples of an unknown…
We consider the sequential composite binary hypothesis testing problem in which one of the hypotheses is governed by a single distribution while the other is governed by a family of distributions whose parameters belong to a known set…
We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…
We propose a new test to address the nonparametric Behrens-Fisher problem involving different distribution functions in the two samples. Our procedure tests the null hypothesis $\mathcal{H}_0: \theta = \frac{1}{2}$, where $\theta = P(X<Y) +…
We explore the problem of distributed Hypothesis Testing (DHT) against independence, focusing specifically on Binary Symmetric Sources (BSS). Our investigation aims to characterize the optimal quantizer among binary linear codes, with the…
This note presents a method that provides optimal monotone conditional error functions for a large class of adaptive two stage designs. The presented method builds on a previously developed general theory for optimal adaptive two stage…
We revisit the fundamental question of simple-versus-simple hypothesis testing with an eye towards computational complexity, as the statistically optimal likelihood ratio test is often computationally intractable in high-dimensional…
Our purpose, is to put forward a change in the paradigm of testing by generalizing a very natural idea exposed by Morris DeGroot (1975) aiming to an approach that is attractive to all schools of statistics, in a procedure better suited for…
The asymptotically optimal hypothesis testing problem with the general sources as the null and alternative hypotheses is studied under exponential-type error constraints on the first kind of error probability. Our fundamental philosophy in…
We study the problem of multiple hypothesis testing (HT) in view of a rejection option. That model of HT has many different applications. Errors in testing of M hypotheses regarding the source distribution with an option of rejecting all…
We study adversarial binary hypothesis testing under memory constraints. The test is a time-invariant randomized finite state machine (FSM) with S states. Associated with each hypothesis is a set of distributions. Given the hypothesis, the…
Recent work has proposed the use of a composite hypothesis Hoeffding test for statistical anomaly detection. Setting an appropriate threshold for the test given a desired false alarm probability involves approximating the false alarm…
The problem of robust binary hypothesis testing is studied. Under both hypotheses, the data-generating distributions are assumed to belong to uncertainty sets constructed through moments; in particular, the sets contain distributions whose…
The achievable error-exponent pairs for the type I and type II errors are characterized in a hypothesis testing setup where the observation consists of independent and identically distributed samples from either a known joint probability…
We study finite-sample inference for the trade-off function of two unknown probability distributions, the function that traces the optimal type I/type II error frontier in binary testing. Given samples from distributions $P$ and $Q$, we…
Multiple hypothesis testing is a central topic in statistics, but despite abundant work on the false discovery rate (FDR) and the corresponding Type-II error concept known as the false non-discovery rate (FNR), a fine-grained understanding…
In confirmatory clinical trials with small sample sizes, hypothesis tests based on asymptotic distributions are often not valid and exact non-parametric procedures are applied instead. However, the latter are based on discrete test…