Related papers: On Hypothesis Testing via a Tunable Loss
We analyze hypotheses tests using classical results on large deviations to compare two models, each one described by a different H\"older Gibbs probability measure. One main difference to the classical hypothesis tests in Decision Theory is…
An active hypothesis testing problem is formulated. In this problem, the agent can perform a fixed number of experiments and then decide on one of the hypotheses. The agent is also allowed to declare its experiments inconclusive if needed.…
The composite binary hypothesis testing problem within the Neyman-Pearson framework is considered. The goal is to maximize the expectation of a nonlinear function of the detection probability, integrated with respect to a given probability…
We consider Bayesian multiple hypothesis problem with independent and identically distributed observations. The classical, Sanov's theorem-based, analysis of the error probability allows one to characterize the best achievable error…
The problem of simple $M-$ary hypothesis testing under a generic performance criterion that depends on arbitrary functions of error probabilities is considered. Using results from convex analysis, it is proved that an optimal decision rule…
Binary hypothesis testing under the Neyman-Pearson formalism is a statistical inference framework for distinguishing data generated by two different source distributions. Privacy restrictions may require the curator of the data or the data…
We study the Neyman-Pearson problem for convex expectations on L^{\infty}(\mu). The existence of the optimal test is given. Without assuming that the level sets of penalty functions are weakly compact, we prove that the optimal tests for…
The trade-off of hypothesis tests on the correlated privacy hypothesis and utility hypothesis is studied. The error exponent of the Bayesian composite hypothesis test on the privacy or utility hypothesis can be characterized by the…
We propose a universal classifier for binary Neyman-Pearson classification where null distribution is known while only a training sequence is available for the alternative distribution. The proposed classifier interpolates between…
We consider symmetric hypothesis testing in quantum statistics, where the hypotheses are density operators on a finite-dimensional complex Hilbert space, representing states of a finite quantum system. We prove a lower bound on the…
Two active hypothesis testing problems are formulated. In these problems, the agent can perform a fixed number of experiments and then decide on one of the hypotheses. The agent is also allowed to declare its experiments inconclusive if…
We point out that the Neyman-Pearson lemma applies to Bayes factors if we consider expected type-1 and type-2 error rates. That is, the Bayes factor is the test statistic that maximises the expected power for a fixed expected type-1 error…
We study the Chernoff-Stein exponent of the following binary hypothesis testing problem: Associated with each hypothesis is a set of channels. A transmitter, without knowledge of the hypothesis, chooses the vector of inputs to the channel.…
Active learning can reduce the number of samples needed to perform a hypothesis test and to estimate the parameters of a model. In this paper, we revisit the work of Chernoff that described an asymptotically optimal algorithm for performing…
The problem of robust hypothesis testing is studied, where under the null and the alternative hypotheses, the data-generating distributions are assumed to be in some uncertainty sets, and the goal is to design a test that performs well…
We propose and study a general method for construction of consistent statistical tests on the basis of possibly indirect, corrupted, or partially available observations. The class of tests devised in the paper contains Neyman's smooth…
The distributed hypothesis testing problem with full side-information is studied. The trade-off (reliability function) between the two types of error exponents under limited rate is studied in the following way. First, the problem is…
In this paper, the Neyman-Pearson lemma for general sublinear expectations is studied. We weaken the assumptions for sublinear expectations in [1] and give a completely new method to study this problem. Applying Mazur-Orlicz Theorem and the…
Neyman and Pearson's theory of testing hypotheses does not warrant minimal epistemic reliability: the feature of driving to true conclusions more often than to false ones. The theory does not protect from the possible negative effects of…
In this paper, we treat an asymptotic hypothesis testing (or state discrimination with asymmetric treatment of errors) between an arbitrary fixed bipartite pure state and the completely mixed state by one-way LOCC, two-way LOCC, and…