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The integration of data and knowledge from several sources is known as data fusion. When data is only available in a distributed fashion or when different sensors are used to infer a quantity of interest, data fusion becomes essential. In…

Machine Learning · Computer Science 2023-12-11 Peng Wu , Tales Imbiriba , Victor Elvira , Pau Closas

It can be important in Bayesian analyses of complex models to construct informative prior distributions which reflect knowledge external to the data at hand. Nevertheless, how much prior information an analyst can elicit from an expert will…

Applications · Statistics 2017-11-10 Xueou Wang , David J. Nott , C. C. Drovandi , Kerrie Mengersen , Michael Evans

Bayesian hypothesis tests leverage posterior probabilities, Bayes factors, or credible intervals to inform data-driven decision making. We propose a framework for power curve approximation with such hypothesis tests. We present a fast…

Methodology · Statistics 2024-10-08 Luke Hagar , Nathaniel T. Stevens

Bayesian inference gets its name from *Bayes's theorem*, expressing posterior probabilities for hypotheses about a data generating process as the (normalized) product of prior probabilities and a likelihood function. But Bayesian inference…

Methodology · Statistics 2024-07-02 Thomas J. Loredo , Robert L. Wolpert

The recent literature on deep learning offers new tools to learn a rich probability distribution over high dimensional data such as images or sounds. In this work we investigate the possibility of learning the prior distribution over neural…

Machine Learning · Statistics 2017-12-19 Alexandre Lacoste , Thomas Boquet , Negar Rostamzadeh , Boris Oreshkin , Wonchang Chung , David Krueger

Machine learning models often perform poorly under subpopulation shifts in the data distribution. Developing methods that allow machine learning models to better generalize to such shifts is crucial for safe deployment in real-world…

Machine Learning · Statistics 2024-03-18 Tim G. J. Rudner , Ya Shi Zhang , Andrew Gordon Wilson , Julia Kempe

A question of some interest is how to characterize the amount of information that a prior puts into a statistical analysis. Rather than a general characterization, we provide an approach to characterizing the amount of information a prior…

Methodology · Statistics 2012-01-10 Michael Evans , Gun Ho Jang

We advocate for a new statistical principle that combines the most desirable aspects of both parameter inference and density estimation. This leads us to the predictively oriented (PrO) posterior, which expresses uncertainty as a…

The inference of deep hierarchical models is problematic due to strong dependencies between the hierarchies. We investigate a specific transformation of the model parameters based on the multivariate distributional transform. This…

Machine Learning · Statistics 2018-12-12 Jakob Knollmüller , Torsten A. Enßlin

Posterior tempering reduces the influence of the likelihood in the calculation of the posterior by raising the likelihood to a fractional power $\alpha$. The resulting power posterior - also known as an $\alpha$-posterior or fractional…

Statistics Theory · Mathematics 2026-01-15 Ruchira Ray , Marco Avella Medina , Cynthia Rush

Making inferences from data streams is a pervasive problem in many modern data analysis applications. But it requires to address the problem of continuous model updating and adapt to changes or drifts in the underlying data generating…

Machine Learning · Computer Science 2017-07-11 Andres Masegosa , Thomas D. Nielsen , Helge Langseth , Dario Ramos-Lopez , Antonio Salmeron , Anders L. Madsen

Regularized linear regression is central to machine learning, yet its high-dimensional behavior with informative priors remains poorly understood. We provide the first exact asymptotic characterization of training and test risks for maximum…

Machine Learning · Statistics 2026-01-28 Malik Tiomoko , Ekkehard Schnoor

To answer the call of introducing more Bayesian techniques to organizational research (e.g., Kruschke, Aguinis, & Joo, 2012; Zyphur & Oswald, 2013), we propose a Bayesian approach for meta-analysis with power prior in this article. The…

Methodology · Statistics 2014-07-30 Zhiyong Zhang , Kaifeng Jiang , Haiyan Liu , In-Sue Oh

Bayesian approaches to data analysis and machine learning are widespread and popular as they provide intuitive yet rigorous axioms for learning from data; see Bernardo and Smith (2004) and Bishop (2006). However, this rigour comes with a…

Methodology · Statistics 2017-01-31 Chris Holmes , Stephen Walker

The BayesPPDSurv (Bayesian Power Prior Design for Survival Data) R package supports Bayesian power and type I error calculations and model fitting using the power and normalized power priors incorporating historical data with for the…

Methodology · Statistics 2024-04-09 Yueqi Shen , Matthew A. Psioda , Joseph G. Ibrahim

We theoretically justify the recent empirical finding of [Teh et al., 2025] that a transformer pretrained on synthetically generated data achieves strong performance on empirical Bayes (EB) problems. We take an indirect approach to this…

Machine Learning · Statistics 2026-02-18 Nick Cannella , Anzo Teh , Yanjun Han , Yury Polyanskiy

A new general framework is presented for implementing complex a priori knowledge, having in mind especially situations where the number of available training data is small compared to the complexity of the learning task. A priori…

Disordered Systems and Neural Networks · Physics 2007-05-23 Joerg C. Lemm

We introduce a prior for the parameters of univariate continuous distributions, based on the Wasserstein information matrix, which is invariant under reparameterisations. We discuss the links between the proposed prior with information…

Statistics Theory · Mathematics 2022-07-28 W. Li , F. J. Rubio

The use of improper priors in the context of Bayesian hierarchical linear mixed models has been studied under the assumption of normality of the random effects. We study the propriety of the posterior under more flexible distributional…

Statistics Theory · Mathematics 2014-09-24 F. J. Rubio

Power posteriors "robustify" standard Bayesian inference by raising the likelihood to a constant fractional power, effectively downweighting its influence in the calculation of the posterior. Power posteriors have been shown to be more…

Statistics Theory · Mathematics 2024-01-22 Ruchira Ray , Marco Avella Medina , Cynthia Rush