Related papers: On combining significances. Some trivial examples
Clinicians and scientists have traditionally focussed on whether their findings will be replicated and are very familiar with the concept. The probability that a replication study yields an effect with the same sign, or the same statistical…
The statistics of the sum of random weights where the number of weights is Poisson distributed has important applications in nuclear physics, particle physics and astrophysics. Events are frequently weighted according to their acceptance or…
We develop criteria sufficient to enable detection of macroscopic coherence where there are not just two macroscopically distinct outcomes for a pointer measurement, but rather a spread of outcomes over a macroscopic range. The criteria…
Using tools from representation theory, we derive expressions for the coincidence rate of partially-distinguishable particles in an interferometry experiment. Our expressions are valid for either bosons or fermions, and for any number of…
A continuous approximation for the results of [1] is obtained. In this approximation the energy distribution is represented in the form of the product of the Gibbs factor and superstatistics factor. The mutual weights of the factors are…
We consider a component of the word statistics known as clump; starting from a finite set of words, clumps are maximal overlapping sets of these occurrences. This parameter has first been studied by Schbath with the aim of counting the…
Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in…
In this paper, we derive an explicit sample size formula based a mixed criterion of absolute and relative errors for estimating means of Poisson random variables.
A Poisson Binomial distribution over $n$ variables is the distribution of the sum of $n$ independent Bernoullis. We provide a sample near-optimal algorithm for testing whether a distribution $P$ supported on $\{0,...,n\}$ to which we have…
The classical Poisson theorem says that if $\xi_1,\xi_2,...$ are i.i.d. 0--1 Bernoulli random variables taking on 1 with probability $p_n\equiv \la/n$ then the sum $S_n=\sum_{i=1}^n\xi_i$ is asymptotically in $n$ Poisson distributed with…
It is shown that for any positive integer k and positive parameter lambda less than 2/k(k+1), the Poisson distribution of order k with parameter lambda has a unique mode, 0. In addition, the Poisson distribution of order 2 has a unique…
The spin-averaged electromagnetic polarizabilities of the hyperons $\Lambda$ and $\Sigma$ are calculated within the one-loop approximation by use of the dispersion theory. The photon and meson couplings to hyperons are determined so as to…
In this note we discuss additional properties of mixed Poisson distributions. We discuss the convergence of mixed Poisson distributions to its mixing distribution for the scaling parameter tending to infinity. Moreover, we obtain a central…
Let X be a Poisson point process of intensity lambda on the real line. A thickening of it is a (deterministic) measurable function f such that the union of X and f(X) is a Poisson point process of intensity lambda' where lambda'>lambda. An…
Statistical significance testing of differences in values of metrics like recall, precision and balanced F-score is a necessary part of empirical natural language processing. Unfortunately, we find in a set of experiments that many commonly…
The robust Poisson method is becoming increasingly popular when estimating the association of exposures with a binary outcome. Unlike the logistic regression model, the robust Poisson method yields results that can be interpreted as risk or…
Research often necessitates of samples, yet obtaining large enough samples is not always possible. When it is, the researcher may use one of two methods for deciding upon the required sample size: rules-of-thumb, quick yet uncertain, and…
Let $S$ be a finite set, and $X_1,\ldots,X_n$ an i.i.d. uniform sample from $S$. To estimate the size $|S|$, without further structure, one can wait for repeats and use the birthday problem. This requires a sample size of the order…
We consider a natural measure of relevance: the reduction in optimal prediction risk in the presence of side information. For any given loss function, this relevance measure captures the benefit of side information for performing inference…
Importance sampling is often used in machine learning when training and testing data come from different distributions. In this paper we propose a new variant of importance sampling that can reduce the variance of importance sampling-based…