Related papers: A Test for the Presence of a Signal, with Multiple…
We describe a statistical hypothesis test for the presence of a signal based on the likelihood ratio statistic. We derive the test for a case of interest and also show that for that case the test works very well, even far out in the tails…
We describe a statistical hypothesis test for the presence of a signal. The test allows the researcher to fix the signal location and/or width a priori, or perform a search to find the signal region that maximizes the signal. The background…
We consider a statistical problem of detection of a signal with unknown energy in a multi-channel system, observed in a Gaussian noise. We assume that the signal can appear in the $k$-th channel with a known small prior probability…
A family of consistent tests, derived from a characterization of the probability generating function, is proposed for assessing Poissonity against a wide class of count distributions, which includes some of the most frequently adopted…
We present a new, analytic, Poisson likelihood derived, technique to account for the statistical uncertainties inherent in simulation samples of limited size. This method has better coverage properties than other techniques, is valid for…
The incorporation of uncertainties to calculations of signal significance in planned experiments is an actual task. Several approaches to this problem are discussed. We present a procedure for taking into account the systematic uncertainty…
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 results of numerical procedure for construction of confidence intervals for parameter of Poisson distribution for signal in the presence of background which has Poisson distribution with known value of parameter are presented. It is shown…
A statistical test is presented to decide whether data are adequately described by probabilistic functions of finite state Markov chains (''hidden Markov models'') as applied in the analysis of ion channel data. Particularly, the test can…
As an application of Stein's method for Poisson approximation, we prove rates of convergence for the tail probabilities of two scan statistics that have been suggested for detecting local signals in sequences of independent random variables…
Results of numerical procedure of constructing confidence intervals for parameter of the Poisson distribution of signal events in the presence of background events with known value of parameter of Poisson distribution are presented. It is…
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…
In this paper, after a discussion of general properties of statistical tests, we present the construction of the most powerful hypothesis test for determining the existence of a new phenomenon in counting-type experiments where the observed…
We study two-receiver Poisson channels using tools derived from stochastic calculus. We obtain a general formula for the mutual information over the Poisson channel that allows for conditioning and the use of auxiliary random variables. We…
Searches for faint signals in counting experiments are often encountered in particle physics and astrophysics, as well as in other fields. Many problems can be reduced to the case of a model with independent and Poisson-distributed signal…
Particle physics experiments such as those run in the Large Hadron Collider result in huge quantities of data, which are boiled down to a few numbers from which it is hoped that a signal will be detected. We discuss a simple probability…
We consider the problem of hypotheses testing with the basic simple hypothesis: observed sequence of points corresponds to stationary Poisson process with known intensity. The alternatives are stationary self-exciting point processes. We…
The empirical probability density function for the conditional distribution of the true value of Poisson distribution parameter on one measurement is constructed by computer experiment. The analysis of the obtained distributions confirms…
The classical Binary Symmetric Channel has a fixed transition probability. We discuss the Binary Symmetric Channel with a variable transition probability that depends on a Poisson distribution. The error rate for this channel is determined…
A definition for the statistical significance of a signal in an experiment is proposed by establishing a correlation between the observed p-value and the normal distribution integral probability, which is suitable for both counting…