Related papers: A frequentist framework of inductive reasoning

We define notions of cautiousness and cautious belief to provide epistemic conditions for iterated admissibility in finite games. We show that iterated admissibility characterizes the behavioral implications of "cautious rationality and…

We introduce a novel approach to inference on parameters that take values in a Riemannian manifold embedded in a Euclidean space. Parameter spaces of this form are ubiquitous across many fields, including chemistry, physics, computer…

For estimating a lower bounded parametric function in the framework of Marchand and Strawderman (2006), we provide through a unified approach a class of Bayesian confidence intervals with credibility $1-\alpha$ and frequentist coverage…

Variational inference is a popular method for estimating model parameters and conditional distributions in hierarchical and mixed models, which arise frequently in many settings in the health, social, and biological sciences. Variational…

We consider the problem of statistical inference on parameters of a target population when auxiliary observations are available from related populations. We propose a flexible empirical Bayes approach that can be applied on top of any…

A substantial generalisation is put forward of the theory of subjective fiducial inference as it was outlined in earlier papers. In particular, this theory is extended to deal with cases where the data are discrete or categorical rather…

Belief systems are often treated as globally consistent sets of propositions or as scalar-valued probability distributions. Such representations tend to obscure the internal structure of belief, conflate external credibility with internal…

Instead of testing for unanimous agreement, I propose learning how broad of a consensus favors one distribution over another (of earnings, productivity, asset returns, test scores, etc.). Specifically, given a sample from each of two…

Many datasets give partial information about an ordering or ranking by indicating which team won a game, which item a user prefers, or who infected whom. We define a continuous spin system whose Gibbs distribution is the posterior…

Bayes' theorem incorporates distinct types of information through the likelihood and prior. Direct observations of state variables enter the likelihood and modify posterior probabilities through consistent updating. Information in terms of…

Uncertainty quantification for estimation through stochastic optimization solutions in an online setting has gained popularity recently. This paper introduces a novel inference method focused on constructing confidence intervals with…

We marshall the arguments for preferring Bayesian hypothesis testing and confidence sets to frequentist ones. We define admissible solutions to inference problems, noting that Bayesian solutions are admissible. We give seven weaker…

We present a distribution optimization framework that significantly improves confidence bounds for various risk measures compared to previous methods. Our framework encompasses popular risk measures such as the entropic risk measure,…

We propose confidence regions with asymptotically correct uniform coverage probability of parameters whose Fisher information matrix can be singular at important points of the parameter set. Our work is motivated by the need for reliable…

Establishing the frequentist properties of Bayesian approaches widens their appeal and offers new understanding. In hypothesis testing, Bayesian model averaging addresses the problem that conclusions are sensitive to variable selection. But…

It is well known that reinforcement learning can be cast as inference in an appropriate probabilistic model. However, this commonly involves introducing a distribution over agent trajectories with probabilities proportional to exponentiated…

This manuscript studies a general approach to construct confidence sets for the solution of stochastic optimization, rendering empirical risk minimization as special cases. Statistical inference for stochastic optimization poses significant…

We study strategic interaction in data-driven games where players face uncertainty about payoff distributions inferred from finite samples. To model calibrated attitudes toward such uncertainty, we formulate distributionally robust games…

Statistical pragmatism embraces all efficient methods in statistical inference. Augmentation of the collected data is used herein to obtain representative population information from a large class of non-representative population's units.…

The presence of interference renders classic Fisher randomization tests infeasible due to nuisance unknowns. To address this issue, we propose imputing the nuisance unknowns and computing Fisher randomization p-values multiple times, then…