Related papers: A Bayesian approach to chiral extrapolations
The Bayesian approach to data analysis provides a powerful way to handle uncertainty in all observations, model parameters, and model structure using probability theory. Probabilistic programming languages make it easier to specify and fit…
A method for sequential inference of the fixed parameters of a dynamic latent Gaussian models is proposed and evaluated that is based on the iterated Laplace approximation. The method provides a useful trade-off between computational…
Decision theories offer principled methods for making choices under various types of uncertainty. Algorithms that implement these theories have been successfully applied to a wide range of real-world problems, including materials and drug…
This work discusses reliability, possible obstacles and the future perspective of chiral extrapolation of lattice results. In the first part, chiral perturbation theory fits to lattice calculations of the nucleon mass are thoroughly…
This paper presents a Bayesian parameter estimation approach and identifiability analysis for a lithium-ion battery model, to determine the uniqueness, evaluate the sensitivity and quantify the uncertainty of a subset of the model…
In this document we are going to derive the equations needed to implement a Variational Bayes estimation of the parameters of the simplified probabilistic linear discriminant analysis (SPLDA) model. This can be used to adapt SPLDA from one…
Consideration of the analytical properties of pion-induced baryon self-energies leads to new functional forms for the extrapolation of light baryon masses. These functional forms reproduce the leading non-analytic behavior of chiral…
The Bradley-Terry model is a popular approach to describe probabilities of the possible outcomes when elements of a set are repeatedly compared with one another in pairs. It has found many applications including animal behaviour, chess…
Statistical modeling is a key component in the extraction of physical results from lattice field theory calculations. Although the general models used are often strongly motivated by physics, many model variations can frequently be…
Chiral perturbation theory is the effective field theory of the strong interactions at low energies. We will give a short introduction to chiral perturbation theory for mesons and will discuss, as an example, the electromagnetic…
It has recently been established that finite-range regularisation in chiral effective field theory enables the accurate extrapolation of modern lattice QCD results to the chiral regime. We review some of the highlights of extrapolations of…
While existing mathematical descriptions can accurately account for phenomena at microscopic scales (e.g. molecular dynamics), these are often high-dimensional, stochastic and their applicability over macroscopic time scales of physical…
Physics increasingly uses Bayesian techniques for systematic data analysis and model-to-data comparison. This paper describes how these methods can be implemented to answer questions of relevance to teaching laboratories. It demonstrates…
It is argued that the Calibrated Bayesian (CB) approach to statistical inference capitalizes on the strength of Bayesian and frequentist approaches to statistical inference. In the CB approach, inferences under a particular model are…
We assess the accuracy of Bayesian polynomial extrapolations from small parameter values, x, to large values of x. We consider a set of polynomials of fixed order, intended as a proxy for a fixed-order effective field theory (EFT)…
Many of the quantities of interest at the precision frontier in particle physics require a good understanding of the strong interaction at low energies. The present talk reviews the theoretical framework used in this context. In particular,…
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…
Dynamical system state estimation and parameter calibration problems are ubiquitous across science and engineering. Bayesian approaches to the problem are the gold standard as they allow for the quantification of uncertainties and enable…
The spectrum of masses from a lattice QCD simulation may be found by fitting exponential functions to correlators of operators possessing the quantum numbers of the particles of interest. The ability of evolutionary algorithms to find…
On the simple model of interacting massless and heavy scalar fields it is demonstrated that the technique of heavy baryon chiral perturbation theory reproduces the results of relativistic theory. Explicit calculations are performed for…