Related papers: Contributed Discussion to Bayesian Solution Uncert…

Uncertainty quantification (UQ) methods for Large Language Models (LLMs) encompass a variety of approaches, with two major types being particularly prominent: information-based, which focus on model confidence expressed as token…

Large Language Models (LLMs) have become indispensable tools across various applications, making it more important than ever to ensure the quality and the trustworthiness of their outputs. This has led to growing interest in uncertainty…

A sandwich likelihood correction is proposed to remedy an inferential limitation of the Bayesian quantile regression approach based on the misspecified asymmetric Laplace density, by leveraging the benefits of the approach. Supporting…

In a real expert system, one may have unreliable, unconfident, conflicting estimates of the value for a particular parameter. It is important for decision making that the information present in this aggregate somehow find its way into use.…

A new method to measure nonlinear dependence between two variables is described using mutual information to analyze the separate linear and nonlinear components of dependence. This technique, which gives an exact value for the proportion of…

Many psychological theories can be operationalized as linear inequality constraints on the parameters of multinomial distributions (e.g., discrete choice analysis). These constraints can be described in two equivalent ways: Either as the…

Deep ensembles can be considered as the current state-of-the-art for uncertainty quantification in deep learning. While the approach was originally proposed as a non-Bayesian technique, arguments supporting its Bayesian footing have been…

This paper presents a new Bayesian framework for quantifying discretization errors in numerical solutions of ordinary differential equations. By modelling the errors as random variables, we impose a monotonicity constraint on the variances,…

We address the estimation problem of the separation of two arbitrarily close incoherent point sources from the quantum Bayesian point of view, i.e., when a prior probability distribution function (PDF) on the separation is available. For…

In this paper we review recently developed methods for nonparametric Bayesian inference for one-dimensional diffusion models. We discuss different possible prior distributions, computational issues, and asymptotic results.

Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…

We present a discussion of the paper "Bayesian cluster analysis: point estimation and credible balls" by Wade and Ghahramani. We believe that this paper contributes substantially to the literature on Bayesian clustering by filling in an…

The recent article "A Bayesian conjugate gradient method" by Cockayne, Oates, Ipsen, and Girolami proposes an approximately Bayesian iterative procedure for the solution of a system of linear equations, based on the conjugate gradient…

A spline chaos expansion, referred to as SCE, is introduced for uncertainty quantification analysis. The expansion provides a means for representing an output random variable of interest with respect to multivariate orthonormal basis…

Uncertainty quantification is an important part of many performance critical applications. This paper provides a simple alternative to existing approaches such as ensemble learning and bayesian neural networks. By directly modeling the loss…

We present a Bayesian perspective on quantifying the uncertainty of graph signals estimated or reconstructed from imperfect observations. We show that many conventional methods of graph signal estimation, reconstruction and imputation, can…

Breakup reactions are one of the favored probes to study loosely bound nuclei, particularly those in the limit of stability forming a halo. In order to interpret such breakup experiments, the continuum discretized coupled channel method is…

This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations. This construction enables the solution of Bayesian inverse problems while accounting for…

In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…

In a Bayesian setting, inverse problems and uncertainty quantification (UQ) - the propagation of uncertainty through a computational (forward) model - are strongly connected. In the form of conditional expectation the Bayesian update…