Related papers: A Practitioner's Guide to Bayesian Inference in Ph…
Plasma diagnostics often employ computerized tomography to estimate emissivity profiles from a finite, and often limited, number of line-integrated measurements. Decades of algorithmic refinement have brought considerable improvements, and…
The parametric bootstrap can be used for the efficient computation of Bayes posterior distributions. Importance sampling formulas take on an easy form relating to the deviance in exponential families and are particularly simple starting…
This is a preliminary version of visual interpretation integrating multiple sensors in SUCCESSOR, an intelligent, model-based vision system. We pursue a thorough integration of hierarchical Bayesian inference with comprehensive physical…
Bayesian inference provides a methodology for parameter estimation and uncertainty quantification in machine learning and deep learning methods. Variational inference and Markov Chain Monte-Carlo (MCMC) sampling methods are used to…
One of the main goals of mathematical modeling in systems medicine related to medical applications is to obtain patient-specific parameterizations and model predictions. In clinical practice, however, the number of available measurements…
This paper introduces the Bayesian Inference Engine (BIE), a general parallel, optimised software package for parameter inference and model selection. This package is motivated by the analysis needs of modern astronomical surveys and the…
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.…
Bayesian estimation is a powerful theoretical paradigm for the operation of quantum sensors. However, the Bayesian method for statistical inference generally suffers from demanding calibration requirements that have so far restricted its…
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…
Mathematical models implemented on a computer have become the driving force behind the acceleration of the cycle of scientific processes. This is because computer models are typically much faster and economical to run than physical…
Simulator-based models are models for which the likelihood is intractable but simulation of synthetic data is possible. They are often used to describe complex real-world phenomena, and as such can often be misspecified in practice.…
This paper offers a comprehensive introduction to Bayesian inference, combining historical context, theoretical foundations, and core analytical examples. Beginning with Bayes' theorem and the philosophical distinctions between Bayesian and…
The quest for precision in parameter estimation is a fundamental task in different scientific areas. The relevance of this problem thus provided the motivation to develop methods for the application of quantum resources to estimation…
The emergent field of probabilistic numerics has thus far lacked clear statistical principals. This paper establishes Bayesian probabilistic numerical methods as those which can be cast as solutions to certain inverse problems within the…
This paper explores the versatility and depth of Bayesian modeling by presenting a comprehensive range of applications and methods, combining Markov chain Monte Carlo (MCMC) techniques and variational approximations. Covering topics such as…
Calibration of computer models is a key step in making inferences, predictions, and decisions for complex science and engineering systems. We formulate and analyze a nonparametric Bayesian methodology for computer model calibration. This…
Determining the best model or models for a particular data set, a process known as Bayesian model comparison, is a critical part of probabilistic inference. Typically, this process assumes a fixed model-space (that is, a fixed set of…
Bayesian statistics and Markov Chain Monte Carlo (MCMC) algorithms have found their place in the field of Cosmology. They have become important mathematical and numerical tools, especially in parameter estimation and model comparison. In…
Reconstructing astrophysical and cosmological fields from observations is challenging. It requires accounting for non-linear transformations, mixing of spatial structure, and noise. In contrast, forward simulators that map fields to…
This introduction to Bayesian statistics presents the main concepts as well as the principal reasons advocated in favour of a Bayesian modelling. We cover the various approaches to prior determination as well as the basis asymptotic…