Using the ζ functional equation and the Hadamard product, an analytical expression for the sum of the reciprocal of the ζ zeros is established. We then demonstrate that on the critical line, |ζ| is convex, and that in the region 0 < <(s) ≤ 0.5, |ζ| has a negative slope, given the RH. In each case, analytical formulae are established, and numerical examples are presented to validate these formulae.

A Bayesian approach to identifying faces from their IR facial images amounts to testing of discrete hypotheses in presence of nuisance variables such as pose, facial expression, and thermal state. We propose an efficient, lowlevel technique for hypothesis pruning, i.e. shortlisting high probability subjects, from given observed image(s). (This subset can be further tested using some detailed hi...

or non-reacting gas mixtures, thus enabling values of (for such mixtures T to be used to guide the equation of state theory for mixtures. This is of interest, for a complete knowledge of the van der Waals forces in mixtures is of profound importance in the application of thermodynamics to chemical equilibria at finite pressures. I J. W. Gibbs, Scientific Papers, Vol. I, p. 87. 2 J. A. Beattie, ...

The aim of statistical inference is to predict the parameters of a population, based on a sample of data. Inferential statistics encompasses the estimation of parameters and model predictions. The present article describes the hypothesis tests or statistical significance tests most commonly used in healthcare research. & 2010 SEICAP. Published by Elsevier España, S.L. All rights reserved.

Document-centric static index pruning methods provide smaller indexes and faster query times by dropping some within-document term information from inverted lists. We present a method of pruning inverted lists derived from the formulation of unigram language models for retrieval. Our method is based on the statistical significance of term frequency ratios: using the two-sample two-proportion (2...

This paper investigates the detection of information hidden by the Least Significant Bit (LSB) matching scheme. In a theoretical context of known image media parameters, two important results are presented. First, the use of hypothesis testing theory allows us to design the Most Powerful (MP) test. Second, a study of the MP test gives us the opportunity to analytically calculate its statistical...

Difference between "Clinical Significance and Statistical Significance" should be kept in mind while interpreting "statistical hypothesis testing" results in clinical research. This fact is already known to many but again pointed out here as philosophy of "statistical hypothesis testing" is sometimes unnecessarily criticized mainly due to failure in considering such distinction. Randomized cont...

These are some notes on a very simple comparative introduction to four basic approaches of statistical inference—Fisher, Neyman–Pearson, Fisher/Neyman–Pearson hybrid, and Bayes—from a course on Quantitative & Statistical Reasoning at OU in Fall 2016. In particular, I hope to give a rough understanding of the differences between the frequentist and Bayesian paradigms, though they are not entirel...

This paper presents algorithms for robustness analysis of Bayesian networks with global neighborhoods. Robust Bayesian inference is the calculation of bounds on posterior values given perturbations in a probabilistic model. We present algorithms for robust inference (including expected utility, expected value and variance bounds) with global perturbations that can be modeled by -contaminated, c...

We introduce two subclasses of convex measures of risk, referred to as entropy coherent and entropy convex measures of risk. Entropy coherent and entropy convex measures of risk are special cases of φ-coherent and φ-convex measures of risk. Contrary to the classical use of coherent and convex measures of risk, which for a given probabilistic model entails evaluating a financial position by cons...