Related papers: Probability distributions for Poisson processes wi…
First-order statistics of scattered light is described using the representation of probability density cloud which visualizes a two-dimensional distribution for complex amplitude. The geometric parameters of the cloud are studied in detail…
Data of the form of event times arise in various applications. A simple model for such data is a non-homogeneous Poisson process (NHPP) which is specified by a rate function that depends on time. We consider the problem of having access to…
Stochastic reaction network models arise in intracellular chemical reactions, epidemiological models and other population process models, and are a class of continuous time Markov chains which have the nonnegative integer lattice as state…
The photon-number distribution between two parts of a given volume is found for an arbitrary photon statistics. This problem is related to the interaction of a light beam with a macroscopic device, for example a diaphragm, that separates…
Observations of present and future X-ray telescopes include a large number of serendipidious sources of unknown types. They are a rich source of knowledge about X-ray dominated astronomical objects, their distribution, and their evolution.…
The Poisson distribution is the probability distribution of the number of independent events in a given period of time. Although the Poisson distribution appears ubiquitously in various stochastic dynamics of gene expression, both as…
Bayesian inference and the use of posterior or posterior predictive probabilities for decision making have become increasingly popular in clinical trials. The current practice in Bayesian clinical trials relies on a hybrid…
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…
An algorithm and numerical code for the up-sampling of a system of particles, from a smaller to a larger number, is described. The method introduces a Poissonian `shot-noise' to the up-sampled distribution, typical of the noise statistics…
It was recently noticed that high-energy scattering processes in QCD have a stochastic nature. An event-by-event scattering amplitude is characterised by a saturation scale which is a random variable. The statistical ensemble of saturation…
This article describes an efficient procedure for computing approximate confidence levels for searches for new particles where the expected signal and background levels are small enough to require the use of Poisson statistics. The results…
This paper presents a new method to estimate systematic errors in the maximum-likelihood regression of count data. The method is applicable in particular to X-ray spectra in situations where the Poisson log-likelihood, or the Cash…
Background: We study the statistical properties of fragment coverage in genome sequencing experiments. In an extension of the classic Lander-Waterman model, we consider the effect of the length distribution of fragments. We also introduce…
Identification of local structure in intensive data -- such as time series, images, and higher dimensional processes -- is an important problem in astronomy. Since the data are typically generated by an inhomogeneous Poisson process, an…
A model describing the coincidental timing of scintillating fibers is developed. Fiber geometry, the rate of scintillation decay together with the mean number, spatial dispersion and attenuation of emitted photons is considered. For 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…
Study of the characteristic properties of charged particle production in hadron-nucleus collisions at high energies, by utilising the approaches from different statistical models is performed.~Predictions from different approaches using the…
We present a novel, easy-to-use method based on the photon-mapping technique to simulate photometric images of moving targets. Realistic images can be created in two passes: photon tracing and image rendering. The nature of light sources,…
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…
Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and…