E-learning has become an efficient and widespread means of education at all levels of human activities. Statistics is no exception. Unfortunately the main focus in statistics teaching is usually paid to the substitution in formulas. Suitable websites can simplify and automate calculations and provide more attention and time to the basic principles of statistics, mathematization of real-life sit...

Consider a decision maker who is responsible to dynamically collect observations so as to enhance his information about an underlying phenomena of interest in a speedy manner while accounting for the penalty of wrong declaration. Due to the sequential nature of the problem, the decision maker relies on his current information state to adaptively select the most “informative” sensing action amon...

The underlying hypothesis of this field is that due to constraints that limit the degrees of freedom of the generative process, data tend to lie near a low dimensional submanifold. This has been empirically observed to be the case, for example, in speech and video data. Although there are many widely used algorithms motivated by this hypothesis, the basic question of testing this hypothesis is ...

It is often the case that we want to infer information using collected data, such as whether two samples can be considered to be from the same population, whether one sample has systematically larger values than another, or whether samples can be considered to be correlated. Such hypotheses may be formally tested using inferential statistics, allowing conclusions to be drawn, allowing the poten...

This paper examines the problem of simultaneously testing many independent multiple hypotheses within the minimum encoding framework. We introduce an efficient coding scheme for nominating the accepted hypotheses in addition to compressing the data given these hypotheses. This formulation reveals an interesting connection between multiple hypothesis testing and mixture modelling with the class ...

Often, biogeography is applied only as a narrative addition to phylogenetic studies and lacks scientific rigour. However, if research questions are framed as hypotheses, biogeographical scenarios become testable. In this review, we explain some problems with narrative biogeography and show how the use of explicit hypotheses is changing understanding of how organisms came to be distributed as th...

This paper reviews important concepts and methods that are useful for hypothesis testing. First, we discuss the Neyman-Pearson framework. Various approaches to optimality are presented, including finite-sample and large-sample optimality. Then, some of the most important methods are summarized, as well as resampling methodology which is useful to set critical values. Finally, we consider the pr...

In most biomedical research, investigators hypothesize about the relationships of various factors, collect data to test those relationships, and try to draw conclusions about those relationships from the data collected. In many cases, investigators test relationships by comparing the average level of a factor between 2 groups or between 1 group and a standard reference. This framework is as tru...

The power of multiple testing procedures can be increased by using weighted p-values (Genovese, Roeder and Wasserman 2005). We derive the optimal weights and we show that the power is remarkably robust to misspecification of these weights. We consider two methods for choosing weights in practice. The first, external weighting, is based on prior information. The second, estimated weighting, uses...

A collaborative distributed binary decision problem is considered. Two statisticians are required to declare the correct probability measure of two jointly distributed memoryless process, denoted by X = (X1, . . . , Xn) and Y n = (Y1, . . . , Yn), out of two possible probability measures on finite alphabets, namely PXY and PX̄Ȳ . The marginal samples given by X and Y n are assumed to be availabl...