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The Poisson distribution is the probability distribution of the number of independent events in a given period of time. Although the Poisson distribution appears ubiquitously in various stochastic dynamics of gene expression, both as…

Statistical Mechanics · Physics 2024-10-02 Julian Lee

An inductive probabilistic classification rule must generally obey the principles of Bayesian predictive inference, such that all observed and unobserved stochastic quantities are jointly modeled and the parameter uncertainty is fully…

Machine Learning · Statistics 2015-03-25 Henrik Nyman , Jie Xiong , Johan Pensar , Jukka Corander

We introduce a new class of priors for Bayesian hypothesis testing, which we name "cake priors". These priors circumvent Bartlett's paradox (also called the Jeffreys-Lindley paradox); the problem associated with the use of diffuse priors…

Statistics Theory · Mathematics 2017-10-26 John T. Ormerod , Michael Stewart , Weichang Yu , Sarah E. Romanes

Given i.i.d. data from an unknown distribution, we consider the problem of predicting future items. An adaptive way to estimate the probability density is to recursively subdivide the domain to an appropriate data-dependent granularity. A…

Statistics Theory · Mathematics 2007-06-13 Marcus Hutter

The Poisson distribution is often used as a standard model for count data. Quite often, however, such data sets are not well fit by a Poisson model because they have more zeros than are compatible with this model. For these situations, a…

Statistics Theory · Mathematics 2008-12-18 M. J. Bayarri , James O. Berger , Gauri S. Datta

The computation of two Bayesian predictive distributions which are discrete mixtures of incomplete beta functions is considered. The number of iterations can easily become large for these distributions and thus, the accuracy of the result…

Statistics Theory · Mathematics 2007-06-13 Jacques Poitevineau , Bruno Lecoutre

In Generalised Bayesian Inference (GBI), the learning rate and hyperparameters of the loss must be estimated. These inference-hyperparameters can't be estimated jointly with the other parameters, from the data, by giving them a prior.…

Methodology · Statistics 2026-05-18 Jeong Eun Lee , Sitong Liu , Geoff K. Nicholls

Iterative imputation, in which variables are imputed one at a time each given a model predicting from all the others, is a popular technique that can be convenient and flexible, as it replaces a potentially difficult multivariate modeling…

Statistics Theory · Mathematics 2012-04-04 Jingchen Liu , Andrew Gelman , Jennifer Hill , Yu-Sung Su

The upsilon distribution, the sum of independent chi random variates and a normal, is introduced. As a special case, the upsilon distribution includes Lecoutre's lambda-prime distribution. The upsilon distribution finds application in…

Statistical Finance · Quantitative Finance 2021-08-17 Steven E. Pav

Although the specification of bivariate probability models using a collection of assumed conditional distributions is not a novel concept, it has received considerable attention in the last decade. In this study, a bivariate…

Methodology · Statistics 2025-03-20 Indranil Ghosh , Mina Norouzirad , Filipe J. Marques

In this article, we investigate posterior convergence of nonparametric binary and Poisson regression under possible model misspecification, assuming general stochastic process prior with appropriate properties. Our model setup and objective…

Statistics Theory · Mathematics 2020-05-04 Debashis Chatterjee , Sourabh Bhattacharya

We study probit regression from a Bayesian perspective and give an alternative form for the posterior distribution when the prior distribution for the regression parameters is the uniform distribution. This new form allows simple Monte…

Methodology · Statistics 2012-03-15 Yuzo Maruyama , William E. Strawderman

A key sticking point of Bayesian analysis is the choice of prior distribution, and there is a vast literature on potential defaults including uniform priors, Jeffreys' priors, reference priors, maximum entropy priors, and weakly informative…

Methodology · Statistics 2017-11-22 Andrew Gelman , Daniel Simpson , Michael Betancourt

Many modern experiments, such as microarray gene expression and genome-wide association studies, present the problem of estimating a large number of parallel effects. Bayesian inference is a popular approach for analyzing such data by…

Methodology · Statistics 2018-10-26 J G Liao , Arthur Berg , Timothy L McMurry

Discrete random probability measures and the exchangeable random partitions they induce are key tools for addressing a variety of estimation and prediction problems in Bayesian inference. Indeed, many popular nonparametric priors, such as…

Statistics Theory · Mathematics 2015-03-03 P. De Blasi , S. Favaro , A. Lijoi , R. H. Mena , I. Pruenster , M. Ruggiero

Bayesian parameter inference depends on a choice of prior probability distribution for the parameters in question. The prior which makes the posterior distribution maximally sensitive to data is called the Jeffreys prior, and it is…

Cosmology and Nongalactic Astrophysics · Physics 2019-02-25 Steen Hannestad , Thomas Tram

In this work, we are concerned with the estimation of the predictive density of a Gaussian random vector where both the mean and the variance are unknown. In such a context, we prove the inadmissibility of the best equivariant predictive…

Statistics Theory · Mathematics 2014-05-27 Aurélie Boisbunon , Yuzo Maruyama

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…

Methodology · Statistics 2020-11-06 Luis E. Nieto-Barajas

We study asymptotically minimax predictive distributions in an infinite sequence model. First, we discuss the connection between the prediction in the infinite sequence model and the prediction in the function model. Second, we construct an…

Statistics Theory · Mathematics 2019-12-06 Keisuke Yano , Fumiyasu Komaki

Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…

Methodology · Statistics 2017-02-28 Shonosuke Sugasawa , Tatsuya Kubokawa