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In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…

Bayesian posterior distributions are widely used for inference, but their dependence on a statistical model creates some challenges. In particular, there may be lots of nuisance parameters that require prior distributions and posterior…

Catalytic prior distributions provide general, easy-to-use, and interpretable specifications of prior distributions for Bayesian analysis. They are particularly beneficial when the observed data are inadequate to stably estimate a complex…

In the recent paper [5], a Bayesian approach for constructing confidence intervals in monotone regression problems is proposed, based on credible intervals. We view this method from a frequentist point of view, and show that it corresponds…

This paper is concerned with Bayesian inferential methods for data from controlled branching processes that account for model robustness through the use of disparities. Under regularity conditions, we establish that estimators built on…

Variable selection and classification are common objectives in the analysis of high-dimensional data. Most such methods make distributional assumptions that may not be compatible with the diverse families of distributions data can take. A…

Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…

Bayesian models provide recursive inference naturally because they can formally reconcile new data and existing scientific information. However, popular use of Bayesian methods often avoids priors that are based on exact posterior…

We revisit empirical Bayes in the absence of a tractable likelihood function, as is typical in scientific domains relying on computer simulations. We investigate how the empirical Bayesian can make use of neural density estimators first to…

Conformal prediction has emerged as a cutting-edge methodology in statistics and machine learning, providing prediction intervals with finite-sample frequentist coverage guarantees. Yet, its interplay with Bayesian statistics, often…

Empirical Bayes methods are widely used for large-scale inference, yet most classical approaches assume homoscedastic observations and focus primarily on posterior mean estimation. We develop a nonparametric empirical Bayes framework for…

The belief network is a well-known graphical structure for representing independences in a joint probability distribution. The methods, which perform probabilistic inference in belief networks, often treat the conditional probabilities…

Bayesian models quantify uncertainty and facilitate optimal decision-making in downstream applications. For most models, however, practitioners are forced to use approximate inference techniques that lead to sub-optimal decisions due to…

Bayesian methods are useful for statistical inference. However, real-world problems can be challenging using Bayesian methods when the data analyst has only limited prior knowledge. In this paper we consider a class of problems, called…

When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated…

Neural networks are popular state-of-the-art models for many different tasks.They are often trained via back-propagation to find a value of the weights that correctly predicts the observed data. Although back-propagation has shown good…

We consider the Bayesian analysis of models in which the unknown distribution of the outcomes is specified up to a set of conditional moment restrictions. The nonparametric exponentially tilted empirical likelihood function is constructed…

We propose a Bayesian approach using improper priors for hierarchical linear mixed models with flexible random effects and residual error distributions. The error distribution is modelled using scale mixtures of normals, which can capture…

Total probability and Bayes formula are two basic tools for using prior information in the Bayesian statistics. In this paper we introduce an alternative tool for using prior information. This new toold enables us to improve some…

One of the goals of probabilistic inference is to decide whether an empirically observed distribution is compatible with a candidate Bayesian network. However, Bayesian networks with hidden variables give rise to highly non-trivial…