Related papers: Bayesian Approach to Inverse Problems: an Applicat…

We present a brief overview of the first global closure test of the fixed parameterisation (MSHT) approach to PDF fitting. We find that the default MSHT20 parameterisation can reproduce the features of the input set in such a closure test…

We present a new regression model for the determination of parton distribution functions (PDF) using techniques inspired from deep learning projects. In the context of the NNPDF methodology, we implement a new efficient computing framework…

Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…

In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…

Geoscientists often solve inverse problems to estimate values of parameters of interest given relevant data sets. Bayesian inference solves these problems by combining probability distributions that describe uncertainties in both…

We present NNPDF3.0, the first set of parton distribution functions (PDFs) determined with a methodology validated by a closure test. NNPDF3.0 uses a global dataset including HERA-II deep-inelastic inclusive cross-sections, the combined…

In this work, we develop a Bayesian framework for solving inverse problems in which the unknown parameter belongs to a space of Radon measures taking values in a separable Hilbert space. The inherent ill-posedness of such problems is…

When using Bayesian inference to support conservative software reliability assessments, it is useful to consider a collection of Bayesian inference problems, with the aim of determining the worst-case value (from this collection) for a…

We present a new public code, FPPDF, to perform global fits of parton distribution functions (PDFs). The fitting methodology follows that implemented by the MSHT collaboration, namely applying a fixed polynomial parameterisation of the PDFs…

Recent work has developed a non-parametric Bayesian approach to the calibration of a computer model, which abstractly amounts to the inversion of a pushforward of stochastic input parameters by a smooth map. The framework has been used in…

We target the problem of accuracy and robustness in causal inference from finite data sets. Some state-of-the-art algorithms produce clear output complete with solid theoretical guarantees but are susceptible to propagating erroneous…

The posterior distribution in a nonparametric inverse problem is shown to contract to the true parameter at a rate that depends on the smoothness of the parameter, and the smoothness and scale of the prior. Correct combinations of these…

Compared to point estimates calculated by standard neural networks, Bayesian neural networks (BNN) provide probability distributions over the output predictions and model parameters, i.e., the weights. Training the weight distribution of a…

The Bayesian approach has proved to be a coherent approach to handle ill posed Inverse problems. However, the Bayesian calculations need either an optimization or an integral calculation. The maximum a posteriori (MAP) estimation requires…

The efficient resolution of Bayesian inverse problems remains challenging due to the high computational cost of traditional sampling methods. In this paper, we propose a novel framework that integrates Conditional Flow Matching (CFM) with a…

Used as priors for Bayesian inverse problems, diffusion models have recently attracted considerable attention in the literature. Their flexibility and high variance enable them to generate multiple solutions for a given task, such as…

We introduce a Bayesian approach to predictive density calibration and combination that accounts for parameter uncertainty and model set incompleteness through the use of random calibration functionals and random combination weights.…

Bayesian approach, as a useful tool for quantifying uncertainties, has been widely used for solving inverse problems of partial differential equations (PDEs). One of the key difficulties for employing Bayesian approach for the issue is how…

The classical approach to inverse problems is based on the optimization of a misfit function. Despite its computational appeal, such an approach suffers from many shortcomings, e.g., non-uniqueness of solutions, modeling prior knowledge,…

We present a first global closure test of the fixed parameterisation (MSHT) approach to PDF fitting. We find that the default MSHT20 parameterisation can reproduce the features of the input set in such a closure test to well within the…