Related papers: On combining significances. Some trivial examples
Statistical significance measures the reliability of a result obtained from a random experiment. We investigate the number of repetitions needed for a statistical result to have a certain significance. In the first step, we consider…
We propose a method to estimate the probability of new physics discovery in future high energy physics experiments. Physics simulation gives both the average numbers $<N_b>$ of background and $<N_s>$ of signal events. We find that the…
We propose a method to estimate the probability of new physics discovery in future high energy physics experiments. Physics simulation gives both the average numbers $<N_b>$ of background and $<N_s>$ of signal events. We find that the…
We present the statistical approach to the combining of signal significances.
When a scientist performs an experiment they normally acquire a set of measurements and are expected to demonstrate that their results are "statistically significant" thus confirming whatever hypothesis they are testing. The main method for…
A definition for the statistical significance by constructing a correlation between the normal distribution integral probability and the p-value observed in an experiment is proposed, which is suitable for both counting experiment and…
We describe a method for estimation of the discovery potential on new physics in planned experiments. The effective significance of signal for given probability of observation is proposed for planned experiments instead of the usual…
We prove the Simons-Johnson theorem for the sums $S_n$ of $m$-dependent random variables, with exponential weights and limiting compound Poisson distribution $\CP(s,\lambda)$. More precisely, we give sufficient conditions for…
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…
Given a periodic point $\omega$ in a $\psi$-mixing shift with countable alphabet, the sequence $\{S_{n}\}$ of random variables counting the number of multiple returns to shrinking cylindrical neighborhoods of $\omega$ is considered.…
A question that comes up repeatedly is how to combine the results of two experiments if all that is known is that one experiment had a n-sigma effect and another experiment had a m-sigma effect. This question is not well-posed: depending on…
It is well known that a binomial $(n,p)$ can be approximated by a Poisson distribution with parameter $np$. The typical approach in undergraduate probability texts is to show a convergence result for the distribution of the binomial as $n$…
Gibbs random fields play an important role in statistics, however, the resulting likelihood is typically unavailable due to an intractable normalizing constant. Composite likelihoods offer a principled means to construct useful…
The Poisson distribution of order $k$ is a special case of a compound Poisson distribution. For $k=1$ it is the standard Poisson distribution. Our main result is a proof that for sufficiently small values of the rate parameter $\lambda$,…
We propose two extensions to existing importance sampling based methods for lossy compression. First, we introduce an importance sampling based compression scheme that is a variant of ordered random coding (Theis and Ahmed, 2022) and is…
Assume that we observe a sample of size n composed of p-dimensional signals, each signal having independent entries drawn from a scaled Poisson distribution with an unknown intensity. We are interested in estimating the sum of the n unknown…
Compound Poisson distributions and signed compound Poisson measures are used for approximation of the Markov binomial distribution. The upper and lower bound estimates are obtained for the total variation, local and Wasserstein norms. In a…
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…
A composite likelihood is an inference function derived by multiplying a set of likelihood components. This approach provides a flexible framework for drawing inference when the likelihood function of a statistical model is computationally…
We examine a generalization of the binomial distribution associated with a strictly increasing sequence of numbers and we prove its Poisson-like limit. Such generalizations might be found in quantum optics with imperfect detection. We…