Related papers: Probability distributions for Poisson processes wi…
We present a method for reconstructing the photon number distribution from the homodyne statistics based on maximization of the likelihood function derived from the exact statistical description of a homodyne experiment. This method…
Various phenomenological models of particle multiplicity distributions are discussed using a general form of the grand canonical partition function. These phenomenological models include a wide range of varied processes such as coherent…
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…
The Mandel probability distribution of one-mode stochastic radiation photocounts is analized. Approximations of n-photon registration probabilities with guaranteed accuracy are obtained in the case when the registration time is sufficiently…
In this paper we propose an estimator of the distribution of events of different kinds in a homogeneous Poisson process. We give an explicit solution for the maximum likelihood estimator of the distribution and derive its strong consistency…
Counting experiments often rely on Monte Carlo simulations for predictions of Poisson expectations. The accompanying uncertainty from the finite Monte Carlo sample size can be incorporated into parameter estimation by modifying the Poisson…
The paper presents a new statistical method that enables the use of systematic errors in the maximum-likelihood regression of integer-count Poisson data to a parametric model. The method is primarily aimed at the characterization of the…
The exact homogenized probability density function, for a photon making a step of length $s$ has been analytically derived for a binary (isotropic-Poisson) statistical mixture with unmatched refractive indexes. The companions, exact,…
Wait-time distributions for the $n$th photo-detection at a detector illuminated by a stationary light beam are studied. Both unconditional measurements, initiated at an arbitrary instant, and conditional measurements, initiated upon a…
We present X-sifter, a software package designed for near-optimal detection of sources in X-ray images and other forms of photon images in the Poisson-noise regime. The code is based on the Poisson-noise-matched filter (Ofek & Zackay),…
Different change-point type models encountered in statistical inference for stochastic processes give rise to different limiting likelihood ratio processes. In a previous paper of one of the authors it was established that one of these…
Pyrosequencing is emerging as one of the important next-generation sequencing technologies. We derive the statistical distributions of this technique in terms of nucleotide probabilities of the target sequences. We give exact distributions…
High-luminosity modern accelerators, like the Relativistic Heavy Ion Collider (RHIC) at BNL and Large Hadron Collider (LHC) at CERN, inherently have event pile-up scenarios which significantly contribute to physics events as a background.…
An iterative algorithm for reconstructing the photon distribution from the random phase homodyne statistics is discussed. This method, derived from the maximum-likelihood approach, yields a positive definite estimate for the photon…
A theory is presented for the photodetection statistics of radiation produced by current fluctuations in a phase-coherent conductor. Deviations are found from the Poisson statistics that would result from a classical current. For detection…
Under mild assumptions the equivalence of the mixed Poisson process with mixing parameter a real-valued random variable to the one with mixing distribution as well as to the mixed Poisson process in the sense of Huang is obtained, and a…
Compared with the start-of-art energy integration detectors (EIDs), photon-counting detectors (PCDs) with energy discrimination capabilities have demonstrated great potentials in various applications of medical x-ray radiography and…
Consider a graph on randomly scattered points in an arbitrary space, with two points $x,y$ connected with probability $\phi(x,y)$. Suppose the number of points is large but the mean number of isolated points is $O(1)$. We give general…
Monte Carlo (MC) simulations allowing to describe photons propagation in statistical mixtures represent an interest that goes way beyond the domain of optics, and can cover, e.g., nuclear reactor physics, image analysis or life science just…
We use Stein's method to obtain bounds on the rate of convergence for a class of statistics in geometric probability obtained as a sum of contributions from Poisson points which are exponentially stabilizing, i.e. locally determined in a…