English
Related papers

Related papers: Simultaneous prediction of independent Poisson obs…

200 papers

The problem is sequence prediction in the following setting. A sequence $x_1,...,x_n,...$ of discrete-valued observations is generated according to some unknown probabilistic law (measure) $\mu$. After observing each outcome, it is required…

Artificial Intelligence · Computer Science 2012-03-20 Daniil Ryabko

A Bayesian approach to variable selection which is based on the expected Kullback-Leibler divergence between the full model and its projection onto a submodel has recently been suggested in the literature. Here we extend this idea by…

Methodology · Statistics 2009-01-30 David Nott , Chenlei Leng

The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the…

Numerical Analysis · Mathematics 2018-02-14 Simon Arridge , Kazufumi Ito , Bangti Jin , Chen Zhang

The Rician distribution, a well-known statistical distribution frequently encountered in fields like magnetic resonance imaging and wireless communications, is particularly useful for describing many real phenomena such as signal process…

Methodology · Statistics 2024-10-30 Jesus Enrique Achire Quispe , Eduardo Ramos , Pedro Luiz Ramos

We consider discrete nonparametric priors which induce Gibbs-type exchangeable random partitions and investigate their posterior behavior in detail. In particular, we deduce conditional distributions and the corresponding Bayesian…

Probability · Mathematics 2008-08-22 Antonio Lijoi , Igor Prünster , Stephen G. Walker

In this paper, we consider objective Bayesian inference of the generalized exponential distribution using the independence Jeffreys prior and validate the propriety of the posterior distribution under a family of structured priors. We…

Methodology · Statistics 2023-09-26 Aojun Li , Keying Ye , Min Wang

Prior sensitivity analysis is a fundamental method to check the effects of prior distributions on the posterior distribution in Bayesian inference. Exploring the posteriors under several alternative priors can be computationally intensive,…

Methodology · Statistics 2025-04-25 Shonosuke Sugasawa

Bayesian posterior distributions are widely used for inference, but their dependence on a statistical model creates some challenges. In particular, there may be lots of nuisance parameters that require prior distributions and posterior…

Statistics Theory · Mathematics 2023-04-12 Nicholas Syring , Ryan Martin

The problem is sequence prediction in the following setting. A sequence x1,..., xn,... of discrete-valued observations is generated according to some unknown probabilistic law (measure) mu. After observing each outcome, it is required to…

Machine Learning · Computer Science 2015-10-19 Daniil Ryabko

We propose an information criterion for multistep ahead predictions. It is also used for extrapolations. For the derivation, we consider multistep ahead predictions under local misspecification. In the prediction, we show that Bayesian…

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

The prior distribution for the unknown model parameters plays a crucial role in the process of statistical inference based on Bayesian methods. However, specifying suitable priors is often difficult even when detailed prior knowledge is…

Methodology · Statistics 2020-03-18 Marcelo Hartmann , Georgi Agiashvili , Paul Bürkner , Arto Klami

Given a random sample from a distribution with density function that depends on an unknown parameter $\theta$, we are interested in accurately estimating the true parametric density function at a future observation from the same…

Statistics Theory · Mathematics 2009-09-29 Mihaela Aslan

We propose a new method for conducting Bayesian prediction that delivers accurate predictions without correctly specifying the unknown true data generating process. A prior is defined over a class of plausible predictive models. After…

Methodology · Statistics 2020-08-24 Ruben Loaiza-Maya , Gael M. Martin , David T. Frazier

This paper is devoted to the multivariate estimation of a vector of Poisson means. A novel loss function that penalises bad estimates of each of the parameters and the sum (or equivalently the mean) of the parameters is introduced. Under…

Statistics Theory · Mathematics 2019-04-25 Emil Aas Stoltenberg , Nils Lid Hjort

Recent decades have seen an interest in prediction problems for which Bayesian methodology has been used ubiquitously. Sampling from or approximating the posterior predictive distribution in a Bayesian model allows one to make inferential…

Machine Learning · Statistics 2017-09-12 Giri Gopalan

Bayesian predictive inference provides a coherent description of entire predictive uncertainty through predictive distributions. We examine several widely used sparsity priors from the predictive (as opposed to estimation) inference…

Statistics Theory · Mathematics 2024-06-03 Veronika Rockova

If the prior probability distributions of all possible hypothetical true means and all possible observed means of a continuous variable are conditional on the universal set of all numbers (i.e., before the nature of a study is known and a…

Methodology · Statistics 2025-06-05 Huw Llewelyn

Let $X| \mu \sim N_p(\mu,v_xI)$ and $Y| \mu \sim N_p(\mu,v_yI)$ be independent p-dimensional multivariate normal vectors with common unknown mean $\mu$. Based on only observing $X=x$, we consider the problem of obtaining a predictive…

Statistics Theory · Mathematics 2007-06-13 Edward I. George , Feng Liang , Xinyi Xu

We propose a new model selection method, the posterior averaging information criterion, for Bayesian model assessment from a predictive perspective. The theoretical foundation is built on the Kullback-Leibler divergence to quantify the…

Methodology · Statistics 2020-09-22 Shouhao Zhou

Loss-based priors assign probability mass to parameter values according to the inferential loss incurred when they are excluded from the parameter space, and provide a general solution for discrete parameters. Extending this idea to…

Methodology · Statistics 2026-04-22 Cristiano Villa