1.1 Deciding between two simple hypotheses: the Neyman-Pearson Lemma. Probability theory is reviewed in Appendix D. Suppose an experiment has a set X of possible outcomes. The outcome has some probability distribution µ defined on X. In statistics, we typically don't know what µ is, but we have hypotheses about what it may be. After making observations we'll try to make a decision between or am...

In the modern Big Data analysis, testing multiple hypotheses simultaneously has been an important tool in analyzing data arising from scientific studies, such as genetics, astronomy, social sciences and many others. The hypotheses can often be grouped together according to the nature of the scientific investigations. For instance, genes can be grouped according to gene pathways; the nearby pixe...

The approach of controlling the false discovery rate (FDR) which is less conservative than controlling the family wise error rate (FWER) has become a new and popular multiple testing procedure in microarray studies. In addition to multiple testing problems the limitation of sample size is another big challenge in this area. This thesis addresses the problem of multiple testing in the context of...

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...

We study the problem of testing composite hypotheses versus composite alternatives, using a convex duality approach. In contrast to classical results obtained by Krafft & Witting [11], where sufficient optimality conditions are obtained via Lagrange duality, we obtain necessary and sufficient optimality conditions via Fenchel duality under some compactness assumptions. This approach also differ...

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...