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In this study, simultaneous predictive distributions for independent Poisson observables were considered and the performance of predictive distributions was evaluated using the Kullback-Leibler (K-L) loss. This study proposes a class of…

Statistics Theory · Mathematics 2024-02-13 Xiao Li

Simultaneous predictive distributions for independent Poisson observables are investigated. A class of improper prior distributions for Poisson means is introduced. The Bayesian predictive distributions based on priors from the introduced…

Statistics Theory · Mathematics 2007-06-13 Fumiyasu Komaki

Simultaneous predictive densities for independent Poisson observables are investigated. The observed data and the target variables to be predicted are independently distributed according to different Poisson distributions parametrized by…

Statistics Theory · Mathematics 2021-05-27 Fumiyasu Komaki

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

This paper deals with the problem of estimating predictive densities of a matrix-variate normal distribution with known covariance matrix. Our main aim is to establish some Bayesian predictive densities related to matricial shrinkage…

Statistics Theory · Mathematics 2017-04-03 Hisayuki Tsukuma , Tatsuya Kubokawa

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 study predictive density estimation under Kullback-Leibler loss in $\ell_0$-sparse Gaussian sequence models. We propose proper Bayes predictive density estimates and establish asymptotic minimaxity in sparse models. A surprise is the…

Statistics Theory · Mathematics 2017-08-01 Gourab Mukherjee , Iain M. Johnstone

This paper discusses predictive densities under the Kullback--Leibler loss for high-dimensional Poisson sequence models under sparsity constraints. Sparsity in count data implies zero-inflation. We present a class of Bayes predictive…

Statistics Theory · Mathematics 2020-09-08 Keisuke Yano , Ryoya Kaneko , Fumiyasu Komaki

We consider nonparametric Bayesian estimation and prediction for nonhomogeneous Poisson process models with unknown intensity functions. We propose a class of improper priors for intensity functions. Nonparametric Bayesian inference with…

Statistics Theory · Mathematics 2021-08-17 Fumiyasu Komaki

Frequentist conditions for asymptotic suitability of Bayesian procedures focus on lower bounds for prior mass in Kullback-Leibler neighbourhoods of the data distribution. The goal of this paper is to investigate the flexibility in criteria…

Statistics Theory · Mathematics 2018-03-19 B. J. K. Kleijn , Y. Y. Zhao

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

We consider the problem of predictive density estimation under Kullback-Leibler loss in a high-dimensional Gaussian model with exact sparsity constraints on the location parameters. We study the first order asymptotic minimax risk of Bayes…

Statistics Theory · Mathematics 2019-05-24 Ujan Gangopadhyay , Gourab Mukherjee

We study prior distributions for Poisson parameter estimation under $L^1$ loss. Specifically, we construct a new family of prior distributions whose optimal Bayesian estimators (the conditional medians) can be any prescribed increasing…

Statistics Theory · Mathematics 2025-05-28 Leighton P. Barnes , Alex Dytso , H. Vincent Poor

We consider estimating the predictive density under Kullback-Leibler loss in an $\ell_0$ sparse Gaussian sequence model. Explicit expressions of the first order minimax risk along with its exact constant, asymptotically least favorable…

Statistics Theory · Mathematics 2015-06-04 Gourab Mukherjee , Iain M. Johnstone

We consider estimating the predictive density under Kullback-Leibler loss in a high-dimensional Gaussian model. Decision theoretic properties of the within-family prediction error -- the minimal risk among estimates in the class…

Statistics Theory · Mathematics 2012-12-04 Gourab Mukherjee , Iain M. Johnstone

This paper deals with the taking into account a given set of realizations as constraints in the Kullback-Leibler minimum principle, which is used as a probabilistic learning algorithm. This permits the effective integration of data into…

Machine Learning · Statistics 2022-05-09 Christian Soize

We consider the fundamental problem of estimating a discrete distribution on a domain of size $K$ with high probability in Kullback-Leibler divergence. We provide upper and lower bounds on the minimax estimation rate, which show that the…

Machine Learning · Statistics 2026-02-23 Dirk van der Hoeven , Julia Olkhovskaia , Tim van Erven

Recent work has attempted to directly approximate the `function-space' or predictive posterior distribution of Bayesian models, without approximating the posterior distribution over the parameters. This is appealing in e.g. Bayesian neural…

Machine Learning · Statistics 2020-11-19 David R. Burt , Sebastian W. Ober , Adrià Garriga-Alonso , Mark van der Wilk

This short note is on a property of the Kullback-Leibler (KL) divergence which indicates that independent Gaussian distributions minimize the KL divergence from given independent Gaussian distributions. The primary purpose of this note is…

Information Theory · Computer Science 2020-12-04 Song Fang , Quanyan Zhu

In a first part, we present a mathematical analysis of a general methodology of a probabilistic learning inference that allows for estimating a posterior probability model for a stochastic boundary value problem from a prior probability…

Machine Learning · Statistics 2022-06-08 Christian Soize
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