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This paper offers a comprehensive introduction to Bayesian inference, combining historical context, theoretical foundations, and core analytical examples. Beginning with Bayes' theorem and the philosophical distinctions between Bayesian and…

Methodology · Statistics 2025-12-08 Juan Sosa , Carlos A. Martínez , Danna Cruz

Federated learning (FL) is a promising framework that models distributed machine learning while protecting the privacy of clients. However, FL suffers performance degradation from heterogeneous and limited data. To alleviate the…

Machine Learning · Computer Science 2023-03-09 Xu Zhang , Wenpeng Li , Yunfeng Shao , Yinchuan Li

One formulation of forensic identification of source problems is to determine the source of trace evidence, for instance, glass fragments found on a suspect for a crime. The current state of the science is to compute a Bayes factor (BF)…

Methodology · Statistics 2020-12-14 Jonathan P Williams , Danica M Ommen , Jan Hannig

Recent methods for deep metric learning have been focusing on designing different contrastive loss functions between positive and negative pairs of samples so that the learned feature embedding is able to pull positive samples of the same…

Computer Vision and Pattern Recognition · Computer Science 2022-11-08 Shichao Kan , Zhiquan He , Yigang Cen , Yang Li , Vladimir Mladenovic , Zhihai He

We overview Bayesian estimation, hypothesis testing, and model-averaging and illustrate how they benefit parametric survival analysis. We contrast the Bayesian framework to the currently dominant frequentist approach and highlight…

Methodology · Statistics 2022-09-13 František Bartoš , Frederik Aust , Julia M. Haaf

This paper focuses on Bayesian inference in a federated learning context (FL). While several distributed MCMC algorithms have been proposed, few consider the specific limitations of FL such as communication bottlenecks and statistical…

Machine Learning · Statistics 2022-11-02 Vincent Plassier , Alain Durmus , Eric Moulines

This study examines the application of Bayesian approach in the context of clinical trials, emphasizing their increasing importance in contemporary biomedical research. While conventional frequentist approach provides a foundational basis…

Methodology · Statistics 2026-01-16 Paramahansa Pramanik , Arnab Kumar Maity , Anjan Mandal , Haley Kate Robinson

Bayesian hierarchical models fit to complex survey data require variance correction for the sampling design, yet applying this correction uniformly harms parameters already protected by the hierarchical structure. We propose the Design…

Methodology · Statistics 2026-03-10 JoonHo Lee

Missing channels in radio-interferometric visibility data can introduce systematic artifacts into the estimated 21-cm power spectrum. A common workaround is to first estimate the two-frequency correlation $C(\Delta\nu)$ and then…

Instrumentation and Methods for Astrophysics · Physics 2026-03-27 Khandakar Md Asif Elahi

The features in high dimensional biomedical prediction problems are often well described with lower dimensional manifolds. An example is genes that are organised in smaller functional networks. The outcome can then be described with the…

Sparse deep learning aims to address the challenge of huge storage consumption by deep neural networks, and to recover the sparse structure of target functions. Although tremendous empirical successes have been achieved, most sparse deep…

Machine Learning · Statistics 2020-11-17 Jincheng Bai , Qifan Song , Guang Cheng

Bayesian inference allows the transparent communication of uncertainty in material flow analyses (MFAs), and a systematic update of uncertainty as new data become available. However, the method is undermined by the difficultly of defining…

Applications · Statistics 2024-03-28 Jiayuan Dong , Jiankan Liao , Xun Huan , Daniel Cooper

Matrix factorization (MF) has become a common approach to collaborative filtering, due to ease of implementation and scalability to large data sets. Two existing drawbacks of the basic model is that it does not incorporate side information…

Machine Learning · Statistics 2014-07-30 Cody Severinski , Ruslan Salakhutdinov

Under a multinormal distribution with arbitrary unknown covariance matrix, the main purpose of this paper is to propose a framework to achieve the goal of reconciliation of Bayesian, frequentist and Fisherian paradigms for the problems of…

Statistics Theory · Mathematics 2019-12-24 Ming-Tien Tsai

We develop a fully Bayesian hierarchical model for trend filtering, itself a new development in nonparametric, univariate regression. The framework more broadly applies to the generalized lasso, but focus is on Bayesian trend filtering. We…

Methodology · Statistics 2015-05-29 Edward A. Roualdes

We address modelling and computational issues for multiple treatment effect inference under many potential confounders. Our main contribution is providing a trade-off between preventing the omission of relevant confounders, while not…

Methodology · Statistics 2025-02-04 Omiros Papaspiliopoulos , David Rossell , Miquel Torrens-i-Dinarès

In several practical applications of federated learning (FL), the clients are highly heterogeneous in terms of both their data and compute resources, and therefore enforcing the same model architecture for each client is very limiting.…

Machine Learning · Computer Science 2023-06-14 Disha Makhija , Joydeep Ghosh , Nhat Ho

Although Bayesian inference is an immensely popular paradigm among a large segment of scientists including statisticians, most applications consider objective priors and need critical investigations (Efron, 2013, Science). While it has…

Statistics Theory · Mathematics 2020-09-11 Abhik Ghosh , Tuhin Majumder , Ayanendranath Basu

Good large sample performance is typically a minimum requirement of any model selection criterion. This article focuses on the consistency property of the Bayes factor, a commonly used model comparison tool, which has experienced a recent…

Statistics Theory · Mathematics 2016-07-04 Siddhartha Chib , Todd A. Kuffner

Bayesian methods are commonly applied to solve image analysis problems such as noise-reduction, feature enhancement and object detection. A primary limitation of these approaches is the computational complexity due to the interdependence of…

Methodology · Statistics 2023-06-01 Konstantinos Bakas , John Kornak , Hernando Ombao