We propose a new approach to sequential testing which is an adaptive (on-line) extension of the (off-line) framework developed in [1]. It relies upon testing of pairs of hypotheses in the case where each hypothesis states that the vector of parameters underlying the distribution of observations belongs to a convex set. The nearly optimal under appropriate conditions test is yielded by a solutio...

By modifying the optimal criterion of Kudo (1967), an alternative theory is developed for incorporating prior probabilities into multiple hypotheses testing. Unlike Kudo’s theory, an explicit optimal test can be obtained. It is shown that the optimal test is a natural extension of some well-known tests such as the maximum likelihood test.

We reexamine observational evidence presented in support of the hypothesis of a sun-climate complexity linking by N. Scafetta and B. J. West, Phys. Rev. Lett. 90, 248701 (2003)10.1103/PhysRevLett.90.248701, which contended that the integrated solar flare index (SFI) and the global temperature anomaly (GTA) both follow Lévy walk statistics with the same waiting-time exponent mu approximately 2.1...

Drawing on some recent results that provide the formalism necessary to definite stationarity for infinite random graphs, this paper initiates the study of statistical and learning questions pertaining to these objects. Specifically, a criterion for the existence of a consistent test for complex hypotheses is presented, generalizing the corresponding results on time series. As an application, it...

Despite a relatively long search for the origin of ebolaviruses, their reservoirs remain elusive. Researchers might have to consider testing alternative hypotheses about how these viruses persist and emerge to advance ebolavirus research. This article aims to encourage researchers to bring forward such hypotheses, to discuss them scientifically and to open alternative research avenues regarding...

We congratulate the authors on a stimulating paper on a very intuitive and general approach to construct hypotheses tests. Restricting the considered class of tests to simple ones determined by a detector function φ, it seems most natural to minimize over φ and maximize over the pair (x, y) ∈ X ×Y where X is the hypothesis and Y the alternative. Particularly, this guarantees that the correspond...

OBJECTIVE The ultimate goal of any genome-scale experiment is to provide a functional interpretation of the results, relating the available genomic information to the hypotheses that originated the experiment. METHODS AND RESULTS Initially, this interpretation has been made on a pre-selection of relevant genes, based on the experimental values, followed by the study of the enrichment in some ...

Rypdal and Rypdal (RR) [1] assert that the hypothesized linking between the Sun and climate complexity, first suggested by Scafetta and West (SW) [2] and developed in subsequent publications [3–6], is not supported by data. However, RR employed Lévy Flight noise in their analysis instead of the Lévy Walk (LW) signal used by SW. In fact, RR focused on the statistics of increments while SW focuse...

Given a discrete-valued sample X1, . . . ,Xn, we wish to decide whether it was generated by a distribution belonging to a family H0, or it was generated by a distribution belonging to a family H1. In this work we assume that all distributions are stationary ergodic and do not make any further assumptions (in particular, no independence or mixing rate assumptions). We find some necessary and som...