Related papers: Bayesian tolerance regions with an application to …

Statistics comes in two main flavors: frequentist and Bayesian. For historical and technical reasons, frequentist statistics has dominated data analysis in the past; but Bayesian statistics is making a comeback at the forefront of science.…

In statistical applications, it is common to encounter parameters supported on a varying or unknown dimensional space. Examples include the fused lasso regression, the matrix recovery under an unknown low rank, etc. Despite the ease of…

Estimation of extreme quantile regions, spaces in which future extreme events can occur with a given low probability, even beyond the range of the observed data, is an important task in the analysis of extremes. Existing methods to estimate…

Contemporary sample size calculations for external validation of risk prediction models require users to specify fixed values of assumed model performance metrics alongside target precision levels (e.g., 95% CI widths). However, due to the…

We consider the problems of hypothesis testing and model comparison under a flexible Bayesian linear regression model whose formulation is closely connected with the linear mixed effect model and the parametric models for SNP set analysis…

The Bayes linear estimator is derived by minimizing the Bayes risk with respect to the squared loss function. Non-unbiased estimators such as ordinary ridge, typical shrinkage, fractional rank, and restricted least squares estimators, as…

A common concern with Bayesian methodology in scientific contexts is that inferences can be heavily influenced by subjective biases. As presented here, there are two types of bias for some quantity of interest: bias against and bias in…

The simultaneous estimation of multiple unknown parameters lies at heart of a broad class of important problems across science and technology. Currently, the state-of-the-art performance in the such problems is achieved by nonparametric…

To the frequentist who computes posteriors, not all priors are useful asymptotically: in this paper Schwartz's 1965 Kullback-Leibler condition is generalised to enable frequentist interpretation of convergence of posterior distributions…

We investigate the frequentist coverage of Bayesian credible sets in a nonparametric setting. We consider a scale of priors of varying regularity and choose the regularity by an empirical Bayes method. Next we consider a central set of…

We develop a method for constructing tolerance bounds for functional data with random warping variability. In particular, we define a generative, probabilistic model for the amplitude and phase components of such observations, which…

We address the common problem of calculating intervals in the presence of systematic uncertainties. We aim to investigate several approaches, but here describe just a Bayesian technique for setting upper limits. The particular example we…

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…

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…

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…

With the rise in popularity of digital Atlases to communicate spatial variation, there is an increasing need for robust small-area estimates. However, current small-area estimation methods suffer from various modeling problems when data are…

Observational astrophysics consists of making inferences about the Universe by comparing data and models. The credible intervals placed on model parameters are often as important as the maximum a posteriori probability values, as the…

Due to their intuitive appeal, Bayesian methods of modeling and uncertainty quantification have become popular in modern machine and deep learning. When providing a prior distribution over the parameter space, it is straightforward to…

We propose optimal Bayesian two-sample tests for testing equality of high-dimensional mean vectors and covariance matrices between two populations. In many applications including genomics and medical imaging, it is natural to assume that…

We propose a novel Bayesian model selection technique on linear mixed-effects models to compare multiple treatments with a control. A fully Bayesian approach is implemented to estimate the marginal inclusion probabilities that provide a…