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At least one unusual event appears in some count datasets. It will lead to a more concentrated (or dispersed) distribution than the Poisson, the gamma, the Weibull, and the Conway-Maxwell-Poisson (CMP) can accommodate. These well-known…
Negative probability values have been widely employed as an indicator of the nonclassicality of quantum systems. Known as a quasiprobability distribution, they are regarded as a useful tool that provides significant insight into the…
Event counts are response variables with non-negative integer values representing the number of times that an event occurs within a fixed domain such as a time interval, a geographical area or a cell of a contingency table. Analysis of…
The seemingly disjoint problems of count and mixture modeling are united under the negative binomial (NB) process. A gamma process is employed to model the rate measure of a Poisson process, whose normalization provides a random probability…
We report experimental observations of correlated-photon statistics in the single-photon detection rate. The usual quantum interference in a two-photon polarization interferometer always accompanies a dip in the single detector counting…
We demonstrate a novel procedure to calibrate neutron detection systems commonly used in standard neutron radiography. This calibration allows determining the uncertainties due to Poisson-like neutron counting statistics for each individual…
Photon number distributions from classical and non-classical light sources have been studied extensively, yet their impact on photoemission processes is largely unexplored. In this article, we present measurements of electron…
The technique of estimating redshifts using photometric rather than spectroscopic observations has recently received great attention due to its simplicity and the accuracy of the results obtained. In this work, we estimate photometric…
We present a new method for determining the sensitivity of X-ray imaging observations, which correctly accounts for the observational biases that affect the probability of detecting a source of a given X-ray flux, without the need to…
Suppose that a compound Poisson process is observed discretely in time and assume that its jump distribution is supported on the set of natural numbers. In this paper we propose a non-parametric Bayesian approach to estimate the intensity…
Neutron and x-ray scattering experiments traditionally rely upon histogrammed data sets, which are analysed using least-squares curve fitting of multiple probability distribution components to quantify separately the various scientific…
X-ray is a ubiquitous imaging modality in clinical diagnostics and industrial inspections, thanks to its high penetration power. Conventional x-ray imaging system, equipped with energy-integrating detectors, collects approximately 1000 to…
We experimentally demonstrate a testing strategy for boson samplers that is based on efficiently computable expressions for the output photon counting distributions binned over multiple optical modes. We apply this method to validate boson…
A theory of joint nonideal measurement of incompatible observables is used in order to assess the relative merits of quantum tomography and certain measurements of generalized observables, with respect to completeness of the obtained…
Quantum sensors can potentially achieve the Heisenberg limit of sensitivity over a large dynamic range using quantum algorithms. The adaptive phase estimation algorithm (PEA) is one example that was proven to achieve such high sensitivities…
The speed of quantum random number generators is a major concern for practical quantum applications. However, the bit extraction process limits the final bit rate due to lack of comparably fast electronics. Here we introduce optical…
An important functional of Poisson random measure is the negative binomial process (NBP). We use NBP to introduce a generalized Poisson-Kingman distribution and its corresponding random discrete probability measure. This random discrete…
Intensity interferometry is a well known method in astronomy. Recently, a related method called incoherent diffractive imaging (IDI) was proposed to apply intensity correlations of x-ray fluorescence radiation to determine the 3D…
Photon counting is a mode of processing astronomical observations of low-signal targets that have been observed using an electron-multiplying charge-coupled device (EMCCD). In photon counting, the EMCCD amplifies the signal, and a…
Photon counting is a cornerstone of quantum optics. Here, we demonstrate precisely counting from 0 to over 9000 photons, beating the Poisson noise limit by at least $4.1~\mathrm{dB}$ across this range. We achieve sub-single-photon precision…