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We review common situations in Bayesian latent variable models where the prior distribution that a researcher specifies differs from the prior distribution used during estimation. These situations can arise from the positive definite…

Methodology · Statistics 2024-11-19 Edgar C. Merkle , Oludare Ariyo , Sonja D. Winter , Mauricio Garnier-Villarreal

Gaussian process regression is a popular Bayesian framework for surrogate modeling of expensive data sources. As part of a broader effort in scientific machine learning, many recent works have incorporated physical constraints or other a…

Machine Learning · Computer Science 2021-01-07 Laura Swiler , Mamikon Gulian , Ari Frankel , Cosmin Safta , John Jakeman

We provide a complete framework for performing infinite-dimensional Bayesian inference and uncertainty quantification for image reconstruction with Poisson data. In particular, we address the following issues to make the Bayesian framework…

Numerical Analysis · Mathematics 2019-10-22 Qingping Zhou , Tengchao Yu , Xiaoqun Zhang , Jinglai Li

Gamma process has been extensively used to model monotone degradation data. Statistical inference for the gamma process is difficult due to the complex parameter structure involved in the likelihood function. In this paper, we derive a…

Methodology · Statistics 2022-12-07 Ancha Xu

Uncovering genuine relationships between a response variable of interest and a large collection of covariates is a fundamental and practically important problem. In the context of Gaussian linear models, both the Bayesian and non-Bayesian…

Statistics Theory · Mathematics 2025-04-11 Jeyong Lee , Minwoo Chae , Ryan Martin

Gaussian graphical modeling has been widely used to explore various network structures, such as gene regulatory networks and social networks. We often use a penalized maximum likelihood approach with the $L_1$ penalty for learning a…

Methodology · Statistics 2017-06-13 Kei Hirose , Hironori Fujisawa , Jun Sese

We use rescaled Gaussian processes as prior models for functional parameters in nonparametric statistical models. We show how the rate of contraction of the posterior distributions depends on the scaling factor. In particular, we exhibit…

Statistics Theory · Mathematics 2009-09-29 Aad van der Vaart , Harry van Zanten

Our paper deals with inferring simulator-based statistical models given some observed data. A simulator-based model is a parametrized mechanism which specifies how data are generated. It is thus also referred to as generative model. We…

Machine Learning · Statistics 2016-01-01 Michael U. Gutmann , Jukka Corander

In a variety of disciplines such as social sciences, psychology, medicine and economics, the recorded data are considered to be noisy measurements of latent variables connected by some causal structure. This corresponds to a family of…

Machine Learning · Computer Science 2014-08-12 Ricardo Silva , Robert B. Gramacy

In a variety of disciplines such as social sciences, psychology, medicine and economics, the recorded data are considered to be noisy measurements of latent variables connected by some causal structure. This corresponds to a family of…

Machine Learning · Computer Science 2010-03-15 Ricardo Silva , Robert B. Gramacy

Bayesian Last Layer (BLL) models focus solely on uncertainty in the output layer of neural networks, demonstrating comparable performance to more complex Bayesian models. However, the use of Gaussian priors for last layer weights in…

Machine Learning · Computer Science 2024-08-08 Jian Xu , Zhiqi Lin , Shigui Li , Min Chen , Junmei Yang , Delu Zeng , John Paisley

We introduce and study a unified Bayesian framework for extended feature allocations which flexibly captures interactions -- such as repulsion or attraction -- among features and their associated weights. We provide a complete Bayesian…

Statistics Theory · Mathematics 2025-03-04 Mario Beraha , Federico Camerlenghi , Lorenzo Ghilotti

We propose a novel Bayesian nonparametric classification model that combines a Gaussian process prior for the latent function with a Dirichlet process prior for the link function, extending the interpretative framework of de Finetti…

Methodology · Statistics 2025-08-26 Marcio Alves Diniz

The Bayesian approach to solving inverse problems relies on the choice of a prior. This critical ingredient allows the formulation of expert knowledge or physical constraints in a probabilistic fashion and plays an important role for the…

Machine Learning · Statistics 2022-11-08 Manuel Marschall , Gerd Wübbeler , Franko Schmähling , Clemens Elster

Variational Bayesian Inference is a popular methodology for approximating posterior distributions over Bayesian neural network weights. Recent work developing this class of methods has explored ever richer parameterizations of the…

The problem of joint estimation of multiple graphical models from high dimensional data has been studied in the statistics and machine learning literature, due to its importance in diverse fields including molecular biology, neuroscience…

Methodology · Statistics 2019-07-04 Peyman Jalali , Kshitij Khare , George Michailidis

Penalized B-splines are routinely used in additive models to describe smooth changes in a response with quantitative covariates. It is typically done through the conditional mean in the exponential family using generalized additive models…

Methodology · Statistics 2020-05-12 Philippe Lambert

This paper presents a novel approach to stochastic mortality modelling by using the Conway--Maxwell--Poisson (CMP) distribution to model death counts. Unlike standard Poisson or negative binomial distributions, the CMP is a more adaptable…

Methodology · Statistics 2026-01-06 Jackie Siaw Tze Wong , Emiliano A. Valdez

We introduce a new empirical Bayes approach for large-scale multiple linear regression. Our approach combines two key ideas: (i) the use of flexible "adaptive shrinkage" priors, which approximate the nonparametric family of scale mixture of…

Methodology · Statistics 2024-06-13 Youngseok Kim , Wei Wang , Peter Carbonetto , Matthew Stephens

Consider a situation of analyzing high-dimensional count data containing an excess of near-zero counts with a small number of moderate or large counts. Assuming that the observations are modeled by a Poisson distribution, we are interested…

Statistics Theory · Mathematics 2025-11-27 Sayantan Paul , Arijit Chakrabarti