Related papers: Concentration inequalities for measures of a Boole…
We develop a prior probability model for temporal Poisson process intensities through structured mixtures of Erlang densities with common scale parameter, mixing on the integer shape parameters. The mixture weights are constructed through…
Non-homogeneous Poisson processes are used in a wide range of scientific disciplines, ranging from the environmental sciences to the health sciences. Often, the central object of interest in a point process is the underlying intensity…
Contrary to standard statistical models, unnormalised statistical models only specify the likelihood function up to a constant. While such models are natural and popular, the lack of normalisation makes inference much more difficult. Here…
Starting from concentration of measure hypotheses on $m$ random vectors $Z_1,\ldots, Z_m$, this article provides an expression of the concentration of functionals $\phi(Z_1,\ldots, Z_m)$ where the variations of $\phi$ on each variable…
Motivated by Alain-Sol Sznitman's interlacement process, we consider the set of $\{0,1\}$-valued processes which can be constructed in an analogous way, namely as a union of sets coming from a Poisson process on a collection of sets. Our…
As it follows from the interrelation of Gamma and Poisson distributions the observed value of asymmetry for Poisson flows of events has the bias. The Monte Carlo experiment confirms the presence of this bias between the observed and initial…
The paper considers the stationary Poisson Boolean model with spherical grains and proposes a family of nonparametric estimators for the radius distribution. These estimators are based on observed distances and radii, weighted in an…
Building on the inequalities for homogeneous tetrahedral polynomials in independent Gaussian variables due to R. Lata{\l}a we provide a concentration inequality for non-necessarily Lipschitz functions $f\colon \R^n \to \R$ with bounded…
Providing accurate theoretical predictions in the Standard Model for processes with polarised electroweak bosons is crucial to understand more in-depth the electroweak-symmetry breaking mechanism and to enhance the sensitivity to potential…
A Bayesian multiple change-point model is proposed to analyse violations of air quality standards by pollutants such as nitrogen oxides (NO2 and NO) and carbon monoxide (CO). The model is built on the assumption that the occurrence of…
We derive the phase space density of bosons from a general boson interferometry formula. We find that the phase space density is connected with the two-particles and the single particle density distribution functions. If the boson density…
Let $\mathfrak{m}$ be a random tessellation in $\mathbf{R}^d$ observed in a bounded Borel subset $W$ and $f(\cdot)$ be a measurable function defined on the set of convex bodies. To each cell $C$ of $\mathfrak{m}$ we associate a point $z(C)$…
A validated simulation model primarily requires performing an appropriate input analysis mainly by determining the behavior of real-world processes using probability distributions. In many practical cases, probability distributions of the…
We utilize the concentration of measure phenomenon to study the large $N$ limit of the $O(N)$ principal chiral model. The partition function in this limit is demonstrated to be that of a free massive theory.
The appropriateness of the Poisson model is frequently challenged when examining spatial count data marked by unbalanced distributions, over-dispersion, or under-dispersion. Moreover, traditional parametric models may inadequately capture…
Various properties of isoperimetric, functional, Transport-Entropy and concentration inequalities are studied on a Riemannian manifold equipped with a measure, whose generalized Ricci curvature is bounded from below. First, stability of…
A measurement of charged-particle distributions sensitive to the properties of the underlying event is presented for an inclusive sample of events containing a Z-boson , decaying to an electron or muon pair. The measurement is based on data…
This article employs the relation between probabilities of two consecutive values of a Poisson random variable to derive conditions for the weak convergence of point processes to a Poisson process. As applications, we consider the starting…
Poisson distributed measurements in inverse problems often stem from Poisson point processes that are observed through discretized or finite-resolution detectors, one of the most prominent examples being positron emission tomography (PET).…
Data on count processes arise in a variety of applications, including longitudinal, spatial and imaging studies measuring count responses. The literature on statistical models for dependent count data is dominated by models built from…