Related papers: Setting Confidence Belts
Bayesian optimization is a coherent, ubiquitous approach to decision-making under uncertainty, with applications including multi-arm bandits, active learning, and black-box optimization. Bayesian optimization selects decisions (i.e.…
This paper explores an approach to Bayesian sample size determination in clinical trials. The approach falls into the category of what is often called "proper Bayesian", in that it does not mix frequentist concepts with Bayesian ones. A…
This paper explores Bayesian estimation for categorical data, focusing on simple yet effective models that provide a foundation for applying more advanced methods accurately and reliably in real-world applications. We begin by revisiting…
This article illustrates how indirect or prior information can be optimally used to construct a prediction region that maintains a target frequentist coverage rate. If the indirect information is accurate, the volume of the prediction…
An advantage of methods that base inference on a posterior distribution is that credible regions are readily obtained. Except in well-specified situations, however, there is no guarantee that such regions will achieve the nominal…
The paper presents a scheme for computing lower and upper bounds on the posterior marginals in Bayesian networks with discrete variables. Its power lies in its ability to use any available scheme that bounds the probability of evidence or…
We study asymptotic frequentist coverage and approximately Gaussian properties of Bayes posterior credible sets in nonlinear inverse problems when a Gaussian prior is placed on the parameter of the PDE. The aim is to ensure valid…
Across the empirical sciences, few statistical procedures rival the popularity of the frequentist t-test. In contrast, the Bayesian versions of the t-test have languished in obscurity. In recent years, however, the theoretical and practical…
We construct uncertainty intervals for weak Poisson signals in the presence of background. We consider the case where a primary experiment yields a realization of the signal plus background, and a second experiment yields a realization of…
Necessary and sufficient conditions of uniform consistency are explored. A hypothesis is simple. Nonparametric sets of alternatives are bounded convex sets in $\mathbb{L}_p$, $p >1$ with "small" balls deleted. The "small" balls have the…
Bayesian estimation is increasingly popular for performing model based inference to support policymaking. These data are often collected from surveys under informative sampling designs where subject inclusion probabilities are designed to…
We investigate the frequentist coverage properties of credible sets resulting in from Gaussian process priors with squared exponential covariance kernel. First we show that by selecting the scaling hyper-parameter using the maximum marginal…
In a sparse stochastic block model with two communities of unequal sizes we derive two posterior concentration inequalities, that imply (1) posterior (almost-)exact recovery of the community structure under sparsity bounds comparable to…
We study the convergence rates of empirical Bayes posterior distributions for nonparametric and high-dimensional inference. We show that as long as the hyperparameter set is discrete, the empirical Bayes posterior distribution induced by…
This paper studies the sparse normal mean models under the empirical Bayes framework. We focus on the mixture priors with an atom at zero and a density component centered at a data driven location determined by maximizing the marginal…
We consider the fixed-confidence best arm identification (FC-BAI) problem in the Bayesian setting. This problem aims to find the arm of the largest mean with a fixed confidence level when the bandit model has been sampled from the known…
We present a computational framework for efficient learning, sampling, and distribution of general Bayesian posterior distributions. The framework leverages a machine learning approach for the construction of normalizing flows for the…
Bayesian methods are increasingly applied in these days in the theory and practice of statistics. Any Bayesian inference depends on a likelihood and a prior. Ideally one would like to elicit a prior from related sources of information or…
The Gaussian theory of errors has been generalized to situations, where the Gaussian distribution and, hence, the Gaussian rules of error propagation are inadequate. The generalizations are based on Bayes' theorem and a suitable measure.…
We consider the problems of hypothesis testing on a probability measure of independent sample, on solution of ill-posed problem, on deconvolution problem and on Poisson mean measure. For all these setups necessary conditions and sufficient…