Related papers: On count data models based on Bernstein functions …
Count-valued autoregressions are widely used to analyse time-series of reported infectious-disease cases because of their close connection with discrete-time transmission models. However, when such models are applied directly to…
Temporal point processes offer a powerful framework for sampling from discrete distributions, yet they remain underutilized in existing literature. We show how to construct, for any target multivariate count distribution with…
We consider the analysis of count data in which the observed frequency of zero counts is unusually large, typically with respect to the Poisson distribution. We focus on two alternative modelling approaches: Over-Dispersion (OD) models, and…
For a sample of absolutely bounded i.i.d. random variables with a continuous density the cumulative distribution function of the sample variance is represented by a univariate integral over a Fourier series. If the density is a polynomial…
This paper develops computationally feasible methods for estimating random effects models in the context of regression modelling of multiple independent time series of discrete valued counts in which there is serial dependence. Given…
Count data appears in various disciplines. In this work, a new method to analyze time series count data has been proposed. The method assumes exponentially decaying covariance structure, a special class of the Mat\'ern covariance function,…
A multidimensional generalization of the Bernstein class of functions and the properties of functions of the introduced class are examined. In particular, a new proof of the integral representation of Bernstein functions of many variables…
For random variables produced through the inverse transform method, approximate random variables are introduced, which are produced by approximations to a distribution's inverse cumulative distribution function. These approximations are…
The derivation and application of Stein identities have received considerable research interest in recent years, especially for continuous or discrete-univariate distributions. In this paper, we complement the existing literature by…
Inverse statistical physics aims at inferring models compatible with a set of empirical averages estimated from a high-dimensional dataset of independently distributed equilibrium configurations of a given system. However, in several…
We consider the Bayesian analysis of models in which the unknown distribution of the outcomes is specified up to a set of conditional moment restrictions. The nonparametric exponentially tilted empirical likelihood function is constructed…
We present a Bayesian non-negative tensor factorization model for count-valued tensor data, and develop scalable inference algorithms (both batch and online) for dealing with massive tensors. Our generative model can handle overdispersed…
In this paper we introduce a bivariate distribution on $\mathbb{R}_{+} \times \mathbb{N}$ arising from a single underlying Markov jump process. The marginal distributions are phase-type and discrete phase-type distributed, respectively,…
This paper introduces Bayesian Flow Networks (BFNs), a new class of generative model in which the parameters of a set of independent distributions are modified with Bayesian inference in the light of noisy data samples, then passed as input…
We propose two novel ways of introducing dependence among Poisson counts through the use of latent variables in a three levels hierarchical model. Marginal distributions of the random variables of interest are Poisson with strict…
The paper considers a Cox process where the stochastic intensity function for the Poisson data model is itself a non-homogeneous Poisson process. We show that it is possible to obtain the marginal data process, namely a non-homogeneous…
We introduce the discrete distribution of a Wiener process range. Rather than finding some basic distributional properties including hazard rate function, moments, Stress-strength parameter and order statistics of this distribution, this…
Motivated by various problems in physics and applied mathematics, we look for constraints and properties of real Fourier-positive functions, i.e. with positive Fourier transforms. Properties of the "Dirac comb" distribution and of its…
We study full Bayesian procedures for high-dimensional linear regression. We adopt data-dependent empirical priors introduced in [1]. In their paper, these priors have nice posterior contraction properties and are easy to compute. Our paper…
The negative binomial distribution has been widely used as a more flexible model than the Poisson distribution for count data. However, when the true data-generating process is Poisson, it is often challenging to distinguish it from a…