Related papers: Frequentist and Bayesian Confidence Intervals

We describe the fundamental difference between the nature of problems in traditional physics and that of many problems arising today in systems biology and other complex settings. The difference hinges on the much larger number of a priori…

Stability selection is a versatile framework for structure estimation and variable selection in high-dimensional setting, primarily grounded in frequentist principles. In this paper, we propose an enhanced methodology that integrates…

Established idea-sets don't update seamlessly. The tension between new and old views of nature is e.g. documented in Galileo's dialogs and now present in many fields. However the science of Bayesian model-selection has made recent strides…

A new method is proposed for the correction of confidence intervals when the original interval does not have the correct nominal coverage probabilities in the frequentist sense. The proposed method is general and does not require any…

Accurate comparisons between theoretical models and experimental data are critical for scientific progress. However, inferred physical model parameters can vary significantly with the chosen physics model, highlighting the importance of…

We propose a construction of frequentist confidence intervals that is effective near unphysical regions and unifies the treatment of two-sided and upper limit intervals. It is rigorous, has coverage, is computationally simple and avoids the…

We empirically show that Bayesian inference can be inconsistent under misspecification in simple linear regression problems, both in a model averaging/selection and in a Bayesian ridge regression setting. We use the standard linear model,…

Physicists have, hitherto, mostly adopted a frequentist conception of probability, according to which probability statements apply only to ensembles. It is argued that we should, instead, adopt an epistemic, or Bayesian conception, in which…

Large-sample Bayesian analogs exist for many frequentist methods, but are less well-known for the widely-used 'sandwich' or 'robust' variance estimates. We review existing approaches to Bayesian analogs of sandwich variance estimates and…

Bayesian inference gets its name from *Bayes's theorem*, expressing posterior probabilities for hypotheses about a data generating process as the (normalized) product of prior probabilities and a likelihood function. But Bayesian inference…

Using a collection of simulated an real benchmarks, we compare Bayesian and frequentist regularization approaches under a low informative constraint when the number of variables is almost equal to the number of observations on simulated and…

We review some aspects of Bayesian and frequentist interval estimation, focusing first on their relative strengths and weaknesses when used in "clean" or "textbook" contexts. We then turn attention to observational-data situations which are…

Inferences about hypotheses are ubiquitous in the cognitive sciences. Bayes factors provide one general way to compare different hypotheses by their compatibility with the observed data. Those quantifications can then also be used to choose…

The practical implementation of Bayesian inference requires numerical approximation when closed-form expressions are not available. What types of accuracy (convergence) of the numerical approximations guarantee robustness and what types do…

Bayesian approaches for handling covariate measurement error are well established, and yet arguably are still relatively little used by researchers. For some this is likely due to unfamiliarity or disagreement with the Bayesian inferential…

The problem of assigning probability distributions which objectively reflect the prior information available about experiments is one of the major stumbling blocks in the use of Bayesian methods of data analysis. In this paper the method of…

Criticisms of so called `subjective probability' come on the one hand from those who maintain that probability in physics has only a frequentistic interpretation, and, on the other, from those who tend to `objectivise' Bayesian theory,…

Bayesian inference paradigms are regarded as powerful tools for solution of inverse problems. However, when applied to inverse problems in physical sciences, Bayesian formulations suffer from a number of inconsistencies that are often…

By representing the range of fair betting odds according to a pair of confidence set estimators, dual probability measures on parameter space called frequentist posteriors secure the coherence of subjective inference without any prior…

As the frontiers of applied statistics progress through increasingly complex experiments we must exploit increasingly sophisticated inferential models to analyze the observations we make. In order to avoid misleading or outright erroneous…