Related papers: Jointly Poisson processes
We obtain a strong law of large numbers and a functional central limit theorem, as $t\to\infty$, for the number of records up to time $t$ and the Lebesgue measure (length) of the subset of the time interval $[0,t]$ during which the Poisson…
We consider time-changed Poisson processes, and derive the governing difference-differential equations (DDE) these processes. In particular, we consider the time-changed Poisson processes where the the time-change is inverse Gaussian, or…
We present a probabilistic model of events in continuous time in which each event triggers a Poisson process of successor events. The ensemble of observed events is thereby modeled as a superposition of Poisson processes. Efficient…
We consider the model selection problem for a large class of time series models, including, multivariate count processes, causal processes with exogenous covariates. A procedure based on a general penalized contrast is proposed. Some…
An unbinned statistical test on cluster-like deviations from Poisson processes for point process data is introduced, presented in the context of time variability analysis of astrophysical sources in count rate experiments. The measure of…
Recent results on particle momentum and spin correlations are discussed in view of the role played by the effects of quantum statistics, including multiboson and coherence phenomena, and final state interaction. Particularly, it is…
This paper addresses the mapping problem. Using a conjugate prior form, we derive the exact theoretical batch multi-object posterior density of the map given a set of measurements. The landmarks in the map are modeled as extended objects,…
Attempts to replicate probabilistic reasoning in expert systems have typically overlooked a critical ingredient of that process. Probabilistic analysis typically requires extensive judgments regarding interdependencies among hypotheses and…
We consider the almost semi-continuous processes defined on a finite Markov chain. The representation of the moment generating functions for the absolute maximum after achievement positive level and for the recovery time are obtained.…
A finite set of quantum observables (positive operator valued measures) is called compatible if these observables are marginals of a some observable, called a joint observable of them. For a given set of compatible observables, their joint…
A consequence of Ornstein theory is that the infinite entropy flows associated with Poisson processes and continuous-time irreducible Markov chains on a finite number of states are isomorphic as measure-preserving systems. We give an…
Scattering moments provide nonparametric models of random processes with stationary increments. They are expected values of random variables computed with a nonexpansive operator, obtained by iteratively applying wavelet transforms and…
Networks play a central role in modern data analysis, enabling us to reason about systems by studying the relationships between their parts. Most often in network analysis, the edges are given. However, in many systems it is difficult or…
We consider a measure given as the continuum limit of a one-dimensional Ising model with long-range translationally invariant interactions. Mathematically, the measure can be described by a self-interacting Poisson driven jump process. We…
Bayesian analyses require that all variable model parameters are given a prior probability distribution. This can pose a challenge for analyses where multiple experiments are combined if these experiments use different parametrisations for…
The origin of non-classical correlations is difficult to identify since the uncertainty principle requires that information obtained about one observable invariably results in the disturbance of any other non-commuting observable. Here,…
An approach to amputation, the process of introducing missing values to a complete dataset, is presented. It allows to construct missingness indicators in a flexible and principled way via copulas and Bernoulli margins and to incorporate…
We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling…
A new family of $n$-dimensional solutions of the Jacobi identities is characterized. Such a family is very general, thus unifying in a common framework many different well-known Poisson systems seemingly unrelated. This unification is not…
The analysis of count data is commonly done using Poisson models. Negative binomial models are a straightforward and readily motivated generalization for the case of overdispersed data, i.e., when the observed variance is greater than…