Related papers: Objective Priors in the Empirical Bayes Framework

Many recently developed Bayesian methods have focused on sparse signal detection. However, much less work has been done addressing the natural follow-up question: how to make valid inferences for the magnitude of those signals after…

When related learning tasks are naturally arranged in a hierarchy, an appealing approach for coping with scarcity of instances is that of transfer learning using a hierarchical Bayes framework. As fully Bayesian computations can be…

Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…

The Robbins estimator is the most iconic and widely used procedure in the empirical Bayes literature for the Poisson model. On one hand, this method has been recently shown to be minimax optimal in terms of the regret (excess risk over the…

Uncertainty quantification is essential when dealing with ill-conditioned inverse problems due to the inherent nonuniqueness of the solution. Bayesian approaches allow us to determine how likely an estimation of the unknown parameters is…

The proposed approach extends the confidence posterior distribution to the semi-parametric empirical Bayes setting. Whereas the Bayesian posterior is defined in terms of a prior distribution conditional on the observed data, the confidence…

In the usual Bayesian setting, a full probabilistic model is required to link the data and parameters, and the form of this model and the inference and prediction mechanisms are specified via de Finetti's representation. In general, such a…

Empirical Bayes methods have been around for a long time and have a wide range of applications. These methods provide a way in which historical data can be aggregated to provide estimates of the posterior mean. This thesis revisits some of…

This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as:…

Given the joint chances of a pair of random variables one can compute quantities of interest, like the mutual information. The Bayesian treatment of unknown chances involves computing, from a second order prior distribution and the data…

High dimensional statistics deals with the challenge of extracting structured information from complex model settings. Compared with the growing number of frequentist methodologies, there are rather few theoretically optimal Bayes methods…

The advent of Generative Artificial Intelligence (GAI) has heralded an inflection point that changed how society thinks about knowledge acquisition. While GAI cannot be fully trusted for decision-making, it may still provide valuable…

It is often claimed that Bayesian methods, in particular Bayes factor methods for hypothesis testing, can deal with optional stopping. We first give an overview, using elementary probability theory, of three different mathematical meanings…

When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp.\ functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by…

Dependent nonparametric processes extend distributions over measures, such as the Dirichlet process and the beta process, to give distributions over collections of measures, typically indexed by values in some covariate space. Such models…

Gaussian empirical Bayes methods usually maintain a precision independence assumption: The unknown parameters of interest are independent from the known standard errors of the estimates. This assumption is often theoretically questionable…

We demonstrate that the principle of maximum relative entropy (ME), used judiciously, can ease the specification of priors in model selection problems. The resulting effect is that models that make sharp predictions are disfavoured,…

Multivariate, heteroscedastic errors complicate statistical inference in many large-scale denoising problems. Empirical Bayes is attractive in such settings, but standard parametric approaches rest on assumptions about the form of the prior…

Nowadays model uncertainty has become one of the most important problems in both academia and industry. In this paper, we mainly consider the scenario in which we have a common model set used for model averaging instead of selecting a…

We develop a semiparametric Bayesian approach for estimating the mean response in a missing data model with binary outcomes and a nonparametrically modelled propensity score. Equivalently we estimate the causal effect of a treatment,…