Related papers: A Bayesian approach to chiral extrapolations
We present a Bayesian approach to machine learning with probabilistic programs. In our approach, training on available data is implemented as inference on a hierarchical model. The posterior distribution of model parameters is then used to…
We analyze the amplitude of radiative charged pion photoproduction within the framework of heavy baryon chiral perturbation theory (HBChPT) and discuss the best experimental setup for the extraction of the charged pion polarizabilities from…
Models with intractable likelihood functions arise in areas including network analysis and spatial statistics, especially those involving Gibbs random fields. Posterior parameter es timation in these settings is termed a doubly-intractable…
We review recent progress in the understanding of low-energy baryon structure by means of chiral perturbation theory. In particular, we discuss the application of this formalism to the description of the quark mass dependence of recent…
There is an increasing amount of literature focused on Bayesian computational methods to address problems with intractable likelihood. One approach is a set of algorithms known as Approximate Bayesian Computational (ABC) methods. One of the…
We address the problem of providing inference from a Bayesian perspective for parameters selected after viewing the data. We present a Bayesian framework for providing inference for selected parameters, based on the observation that…
An introduction to methods of effective field theory is given. Examples are presented, including Rayleigh scattering from nonrelativistic quantum mechnics, chiral perturbation theory/QCD as well as electromagnetic and weak interactions of…
We report on a novel scheme based on the chiral Lagrangian. It is used to analyze pion-nucleon scattering, pion photoproduction, and nucleon Compton scattering. Subthreshold partial-wave amplitudes are calculated in chiral perturbation…
We derive an exact and efficient Bayesian regression algorithm for piecewise constant functions of unknown segment number, boundary location, and levels. It works for any noise and segment level prior, e.g. Cauchy which can handle outliers.…
After making some general remarks, I consider two examples that illustrate the use of Bayesian Probability Theory. The first is a simple one, the physicist's favorite "toy," that provides a forum for a discussion of the key conceptual issue…
This paper focuses on utilizing two different Bayesian methods to deal with a variety of toy problems which occur in data analysis. In particular we implement the Variational Bayesian and Nested Sampling methods to tackle the problems of…
We show that the interplay of chiral effective field theory and lattice QCD can be used in the evaluation of so-called disconnected diagrams, which appear in the study of the isoscalar and isovector channels of pion-pion scattering and have…
We explore the chiral aspects of extrapolation of observables calculated within lattice QCD, using the nucleon magnetic moments as an example. Our analysis shows that the biggest effects of chiral dynamics occur for quark masses…
Bayesian models quantify uncertainty and facilitate optimal decision-making in downstream applications. For most models, however, practitioners are forced to use approximate inference techniques that lead to sub-optimal decisions due to…
We focus on improving the accuracy of an approximate model of a multiscale dynamical system that uses a set of parameter-dependent terms to account for the effects of unresolved or neglected dynamics on resolved scales. We start by…
The current standard Bayesian approach to model calibration, which assigns a Gaussian process prior to the discrepancy term, often suffers from issues of unidentifiability and computational complexity and instability. When the goal is to…
We introduce a novel rule-based approach for handling regression problems. The new methodology carries elements from two frameworks: (i) it provides information about the uncertainty of the parameters of interest using Bayesian inference,…
Several physical problems in particle physics, nuclear physics, and astrophysics require information from non-perturbative QCD to gain a full understanding. In some cases the most reliable technique for quantitative results is to carry out…
Implementing Bayesian inference is often computationally challenging in applications involving complex models, and sometimes calculating the likelihood itself is difficult. Synthetic likelihood is one approach for carrying out inference…
The estimation of cosmological parameters from precision observables is an important industry with crucial ramifications for particle physics. This article discusses the statistical methods presently used in cosmological data analysis,…