We introduce a theoretical framework for performing statistical hypothesis testing simultaneously over a fairly general, possibly uncountably infinite, set of null hypotheses. This extends the standard statistical setting for multiple hypotheses testing, which is restricted to a finite set. This work is motivated by numerous modern applications where the observed signal is modeled by a stochast...

We consider the problem of hypotheses testing with the basic simple hypothesis: observed sequence of points corresponds to stationary Poisson process with known intensity against a composite one-sided parametric alternative that this is a self-correcting point process. The underlying family of measures is locally asymptotically quadratic and we describe the behavior of score function, likelihoo...

Some thoughts on the calculation of quantitative probabilities of edge detection, for investigation during the 3D object recognition and localisation project. See also Tina memo 2006-007.

Do two data samples come from different distributions? Recent studies of this fundamental problem focused on embedding probability distributions into sufficiently rich characteristic Reproducing Kernel Hilbert Spaces (RKHSs), to compare distributions by the distance between their embeddings. We show that Regularized Maximum Mean Discrepancy (RMMD), our novel measure for kernel-based hypothesis ...

It is crucial to identify the most appropriate hypotheses if one is to apply probabilistic reasoning to evaluate and properly understand the impact of evidence. Subtle changes to the choice of a prosecution hypothesis can result in drastically different posterior probabilities to a defence hypothesis from the same evidence. To illustrate the problem we consider a real case in which probabilisti...

We study the stability of the classical optimal sequential probability ratio test based on independent identically distributed observations X1, X2, . . . when testing two simple hypotheses about their common density f : f = f0 versus f = f1. As a functional to be minimized, it is used a weighted sum of the average (under f0) sample number and the two types error probabilities. We prove that the...

To ensure the conformance of an implementation under test (in the following IUT) with respect to a specification requires, in general, the application of an infinite number of tests. In order to use finite test suites, most testing methodologies add some feasible hypotheses about the behavior of the IUT. Since these methodologies are designed for considering a fix set of hypotheses, they usuall...

The anomaly detection and localization problem can be treated as a multiple hypotheses testing (MHT) problem in the Bayesian framework. The Bayesian test with the 0-1 loss function is a standard solution for this problem, but the alternative hypotheses have quite different importance in practice. The 0-1 loss function does not reflect this fact while the quadratic loss function is more appropri...

The purpose of this paper is to examine the effects of inflation and operating cycle on cash holding in Tehran Stock Exchange in the period 2010 to 2014.The sample is comprised of 103 companies which are selected by systematic elimination method and total of 515 year-firm collected. In this study for testing the hypothesis is used of linear regression and correlation. To analyse data and test h...

In hypotheses testing, such as other statistical problems, we may confront imprecise concepts. One case is a situation in which hypotheses are imprecise. In this paper, we redefine some concepts about fuzzy hypotheses testing, and then we introduce the sequential probability ratio test for fuzzy hypotheses testing. Finally, we give some examples. Mathematics Subject Classification: 03E72, 62F03...