Related papers: Improved iterative Bayesian unfolding
Distribution regression has recently attracted much interest as a generic solution to the problem of supervised learning where labels are available at the group level, rather than at the individual level. Current approaches, however, do not…
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…
While Robert and Rousseau (2010) addressed the foundational aspects of Bayesian analysis, the current chapter details its practical aspects through a review of the computational methods available for approximating Bayesian procedures.…
Modern regression applications can involve hundreds or thousands of variables which motivates the use of variable selection methods. Bayesian variable selection defines a posterior distribution on the possible subsets of the variables…
We consider the problem of Bayesian regression with trustworthy uncertainty quantification. We define that the uncertainty quantification is trustworthy if the ground truth can be captured by intervals dependent on the predictive…
Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…
A series of monte carlo studies were performed to compare the behavior of some alternative procedures for reasoning under uncertainty. The behavior of several Bayesian, linear model and default reasoning procedures were examined in the…
This paper proposes a novel uncertainty quantification framework for computationally demanding systems characterized by a large vector of non-Gaussian uncertainties. It combines state-of-the-art techniques in advanced Monte Carlo sampling…
Deep neural networks have achieved impressive results on a wide variety of tasks. However, quantifying uncertainty in the network's output is a challenging task. Bayesian models offer a mathematical framework to reason about model…
Uncertainty estimation in deep models is essential in many real-world applications and has benefited from developments over the last several years. Recent evidence suggests that existing solutions dependent on simple Gaussian formulations…
Frequentist and likelihood methods of inference based on the multivariate skew-normal model encounter several technical difficulties with this model. In spite of the popularity of this class of densities, there are no broadly satisfactory…
We describe an iterative unfolding method for experimental data, making use of a regularization function. The use of this function allows one to build an improved normalization procedure for Monte Carlo spectra, unbiased by the presence of…
Bayesian analyses are often performed using so-called noninformative priors, with a view to achieving objective inference about unknown parameters on which available data depends. Noninformative priors depend on the relationship of the data…
Three different inferential problems related to a two dimensional categorical data from a Bayesian perspective have been discussed in this article. Conjugate prior distribution with symmetric and asymmetric hyper parameters are considered.…
Two non-intrusive uncertainty propagation approaches are proposed for the performance analysis of engineering systems described by expensive-to-evaluate deterministic computer models with parameters defined as interval variables. These…
Bayesian quadrature is a probabilistic, model-based approach to numerical integration, the estimation of intractable integrals, or expectations. Although Bayesian quadrature was popularised already in the 1980s, no systematic and…
The main contribution of this paper is to develop a hierarchical Bayesian formulation of PINNs for linear inverse problems, which is called BPINN-IP. The proposed methodology extends PINN to account for prior knowledge on the nature of the…
Clustering is a crucial task in various domains of knowledge, including medicine, epidemiology, genomics, environmental science, economics, and visual sciences, among others. Methodologies for inferring the number of clusters have often…
In this review, we assess the use of Bayesian methods in model predictive control (MPC), focusing on neural-network-based modeling, control design, and uncertainty quantification. We systematically analyze individual studies and how they…
We propose a Bayesian elastic net that uses empirical likelihood and develop an efficient tuning of Hamiltonian Monte Carlo for posterior sampling. The proposed model relaxes the assumptions on the identity of the error distribution,…