WASP: Scalable Bayes via barycenters of subset posteriors

Bayes via barycenters of subset posteriors

THE EMPIRICAL BAYES METHOD OF ANALYSIS OF A SERIES OF EXPERIMENTS

The classical method of analysis of a series of experiments is somewhat involved in being conditional on various, occasionally unrealistic, assumptions such as homogeneity of variances of experimental error, lack of interactions of treatments and places,etc. In this work, we adopt a Bayesian view to account for such heterogeneities. Our appoach is illustrated by a real series of experiment...

Empirical Bayes interval estimates that are conditionally equal to unadjusted confidence intervals or to default prior credibility intervals.

Problems involving thousands of null hypotheses have been addressed by estimating the local false discovery rate (LFDR). A previous LFDR approach to reporting point and interval estimates of an effect-size parameter uses an estimate of the prior distribution of the parameter conditional on the alternative hypothesis. That estimated prior is often unreliable, and yet strongly influences the post...

Group invariant inferred distributions via noncommutative probability

Abstract: One may consider three types of statistical inference: Bayesian, frequentist, and group invariance-based. The focus here is on the last method. We consider the Poisson and binomial distributions in detail to illustrate a group invariance method for constructing inferred distributions on parameter spaces given observed results. These inferred distributions are obtained without using Ba...

PAC-Bayes Risk Bounds for Stochastic Averages and Majority Votes of Sample-Compressed Classifiers

We propose a PAC-Bayes theorem for the sample-compression setting where each classifier is described by a compression subset of the training data and a message string of additional information. This setting, which is the appropriate one to describe many learning algorithms, strictly generalizes the usual data-independent setting where classifiers are represented only by data-independent message...