Related papers: Valid and efficient imprecise-probabilistic infere…

We present a general framework for Bayesian inference of causal effects that delivers provably robust inferences founded on design-based randomization of treatments. The framework involves fixing the observed potential outcomes and forming…

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…

The standard approach to Bayesian inference is based on the assumption that the distribution of the data belongs to the chosen model class. However, even a small violation of this assumption can have a large impact on the outcome of a…

Sensitivity forecasts inform the design of experiments and the direction of theoretical efforts. To arrive at representative results, Bayesian forecasts should marginalize their conclusions over uncertain parameters and noise realizations…

A crucial step in fitting a regression model to data is determining the model's structure, i.e., the subset of explanatory variables to be included. However, the uncertainty in this step is often overlooked due to a lack of satisfactory…

Inference is an integral part of probabilistic topic models, but is often non-trivial to derive an efficient algorithm for a specific model. It is even much more challenging when we want to find a fast inference algorithm which always…

Approximate Bayesian computing is a powerful likelihood-free method that has grown increasingly popular since early applications in population genetics. However, complications arise in the theoretical justification for Bayesian inference…

A rich set of frequentist model averaging methods has been developed, but their applications have largely been limited to point prediction, as measuring prediction uncertainty in general settings remains an open problem. In this paper we…

Bayesian inference provides a rigorous framework to encapsulate our knowledge and uncertainty regarding various physical quantities in a well-defined and self-contained manner. Utilising modern tools, such Bayesian models can be constructed…

Meta-analysis based on only a few studies remains a challenging problem, as an accurate estimate of the between-study variance is apparently needed, but hard to attain, within this setting. Here we offer a new approach, based on the…

Fuzzy data, prevalent in social sciences and other fields, capture uncertainties arising from subjective evaluations and measurement imprecision. Despite significant advancements in fuzzy statistics, a unified inferential regression-based…

Total probability and Bayes formula are two basic tools for using prior information in the Bayesian statistics. In this paper we introduce an alternative tool for using prior information. This new toold enables us to improve some…

The inferential models (IM) framework provides prior-free, frequency-calibrated, posterior probabilistic inference. The key is the use of random sets to predict unobservable auxiliary variables connected to the observable data and unknown…

Predictive uncertainty quantification is crucial for reliable decision-making in various applied domains. Bayesian neural networks offer a powerful framework for this task. However, defining meaningful priors and ensuring computational…

We propose a simple approach that provides accurate uncertainty quantification for Bayesian inference in misspecified or approximate models, and for generalized (Gibbs) posteriors. While existing solutions in this context are based on…

This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as:…

Statistical inference for extreme values of random events is difficult in practice due to low sample sizes and inaccurate models for the studied rare events. If prior knowledge for extreme values is available, Bayesian statistics can be…

Inferential models have been proposed for valid and efficient prior-free probabilistic inference. As it gradually gained popularity, this theory is subject to further developments for practically challenging problems. This paper considers…

In recent years, empirical Bayesian (EB) inference has become an attractive approach for estimation in parametric models arising in a variety of real-life problems, especially in complex and high-dimensional scientific applications.…

As machine learning-based prediction systems are increasingly used in high-stakes situations, it is important to understand how such predictive models will perform upon deployment. Distribution-free uncertainty quantification techniques…