Related papers: Binary Hypothesis Testing with Deterministic Finit…
We study high-dimensional asymptotic performance limits of binary supervised classification problems where the class conditional densities are Gaussian with unknown means and covariances and the number of signal dimensions scales faster…
We use the exact finite sample likelihood and statistical decision theory to answer questions of ``why?'' and ``what should you have done?'' using data from randomized experiments and a utility function that prioritizes safety over…
In this work, we consider a binary hypothesis testing problem involving a group of human decision-makers. Due to the nature of human behavior, each human decision-maker observes the phenomenon of interest sequentially up to a random length…
In using the Bayesian network (BN) to construct the complex multistate system's reliability model as described in Part I, the memory storage requirements of the node probability table (NPT) will exceed the random access memory (RAM) of the…
We provide a novel analysis of Wald's sequential probability ratio test based on information theoretic measures for symmetric thresholds, symmetric noise, and equally likely hypotheses under the assumption that the test exactly terminates…
Consider the problem of distributed binary hypothesis testing with two terminals, where the decision is made at one of them (the "receiver"). We study the exponent of the error probability of the second type. Previously, an achievable…
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,…
Probabilistic and set-based methods are two approaches for model invalidation, parameter and state estimation. Both classes of methods use different types of data, i.e. deterministic or probabilistic data, which allow different statements…
In the Bayesian approach to sequential decision making, exact calculation of the (subjective) utility is intractable. This extends to most special cases of interest, such as reinforcement learning problems. While utility bounds are known to…
Sequential methods for quantum hypothesis testing offer significant advantages over fixed-length approaches, which rely on a predefined number of state copies. Despite their potential, these methods remain underexplored for unambiguous…
In this paper we suggest two statistical hypothesis tests for the regression function of binary classification based on conditional kernel mean embeddings. The regression function is a fundamental object in classification as it determines…
Let $X_1,X_2,...$ be a discrete-time stochastic process with a distribution $P_\theta$, $\theta\in\Theta$, where $\Theta$ is an open subset of the real line. We consider the problem of testing a simple hypothesis $H_0:$ $\theta=\theta_0$…
The forward prediction problem for a binary time series $\{X_n\}_{n=0}^{\infty}$ is to estimate the probability that $X_{n+1}=1$ based on the observations $X_i$, $0\le i\le n$ without prior knowledge of the distribution of the process…
We introduce a testing-by-betting framework that leverages predictions on unlabeled data to enhance the power of sequential hypothesis testing. Given limited samples from the joint distribution of $(X,Y)$, and additional unlabeled samples…
This paper explores the multiple testing problem for sparse high-dimensional data with binary outcomes. We propose novel empirical Bayes multiple testing procedures based on a spike-and-slab posterior and then evaluate their performance in…
This paper deals with the problem of simultaneously making many (M) binary decisions based on one realization of a random data matrix X. M is typically large and X will usually have M rows associated with each of the M decisions to make,…
This work deals with a general problem of testing multiple hypotheses about the distribution of a discrete-time stochastic process. Both the Bayesian and the conditional settings are considered. The structure of optimal sequential tests is…
A resurgence of interest in multiple hypothesis testing has occurred in the last decade. Motivated by studies in genomics, microarrays, DNA sequencing, drug screening, clinical trials, bioassays, education and psychology, statisticians have…
Detection rules have traditionally been designed for rational agents that minimize the Bayes risk (average decision cost). With the advent of crowd-sensing systems, there is a need to redesign binary hypothesis testing rules for behavioral…
Hybrid mechanistic models, physical priors with learned residuals, promise to reduce the data required for good decisions, but have no computable criterion to test this. We characterize the value of mechanistic priors in sequential…