Related papers: On the Combining Significances
Three variants of the statistical complexity function, which is used as a criterion in the problem of detection of a useful signal in the signal-noise mixture, are considered. The probability distributions maximizing the considered variants…
We describe a statistical hypothesis test for the presence of a signal based on the likelihood ratio statistic. We derive the test for a special case of interest. We study extensions of the test to cases where there are multiple channels…
We offer several new summation identities involving harmonic numbers, odd harmonic numbers, and Fibonacci numbers. Our results are derived using three different approaches: partial summation, polynomial identities and binomial…
In this chapter, a statistical measure of complexity is introduced and some of its properties are discussed. Also, some straightforward applications are shown.
Bayesian, classical, and extended maximum likelihood approaches to estimation of upper limits in experiments with small numbers of signal events are surveyed. The discussion covers only experiments whose outcomes are well described by a…
A suggestion is made for improving the Feldman Cousins method of estimating signal counts in the presence of background. The method concentrates on finding essential information about the signal and ignoring extraneous information about…
This paper presents a new mathematical signal transform that is especially suitable for decoding information related to non-rigid signal displacements. We provide a measure theoretic framework to extend the existing Cumulative Distribution…
In this article, we give a formula for the generalization of the binomial coefficient to the complex numbers as a linear combination of $\sinc$ functions. We then give a general formula to compute the integral on the real line of the…
A new method is introduced to obtain a strong signal by the interference of weak signals in noisy channels. The method is based on the interference of 1/f noise from parallel channels. One realization of stochastic interference is the…
We describe recent advances in the study of random analogues of combinatorial theorems.
Numerous signals in relevant signal processing applications can be modeled as a sum of complex exponentials. Each exponential term entails a particular property of the modeled physical system, and it is possible to define families of…
Statistically resolving the underlying haplotype pair for a genotype measurement is an important intermediate step in gene mapping studies, and has received much attention recently. Consequently, a variety of methods for this problem have…
In this expository paper we give an overview of some statistical methods for the monitoring of social networks. We discuss the advantages and limitations of various methods as well as some relevant issues. One of our primary contributions…
We discuss how to determine and combine upper limits based on observed events and estimated backgrounds with a Bayesian method, when insignificant signals are observed in independent measurements. In addition to some general features…
The distribution function of the sum of i.i.d. random variables of the special form is considered. Such sum describes messages posterior probabilities for random coding in binary symmetric channel. Close non-asymptotic lower and upper…
A common signal is defined for any two signals which have non-zero correlation. A mathematical method is provided to extract the best obtainable common signal between the two signals. This analysis is extended to extracting common signal…
In this paper we investigate congruence relationships of particular finite generalized harmonic numbers sums. We suggest more transparent and simpler method to analyse these sums and present several additional results for certain special…
The purpose of this paper is twofold. First, the definition of new statistical convergence with Fibonacci sequence is given and some fundamental properties of statistical convergence are examined. Second, approximation theory worked as a…
A statistical estimation model with qualitative input provides a mechanism to fuse human intuition in the form of qualitative information into a statistical model. We investigate the statistical properties of this model and devise a…
The main phases of applied statistical work are discussed in general terms. The account starts with the clarification of objectives and proceeds through study design, measurement and analysis to interpretation. An attempt is made to extract…