BayesicFitting, a PYTHON Toolbox for Bayesian Fitting and Evidence Calculation

arXiv (Cornell University)

Abstract

BayesicFitting is a comprehensive, general-purpose toolbox for simple and standardized model fitting. Its fitting options range from simple least-squares methods, via maximum likelihood to fully Bayesian inference, working on a multitude of available models. BayesicFitting is open source and has been in development and use since the 1990s. It has been applied to a variety of science applications, chiefly in astronomy. BayesicFitting consists of a collection of PYTHON classes that can be combined to solve quite complicated inference problems. Amongst the classes are models, fitters, priors, error distributions, engines, samples, and of course NestedSampler, our general-purpose implementation of the nested sampling algorithm. Nested sampling is a novel way to perform Bayesian calculations. It can be applied to inference problems, that consist of a parameterized model to fit measured data to. NestedSampler calculates the Bayesian evidence as the numeric integral over the posterior probability of (hyper)parameters of the problem. The solution in terms of the parameters is obtained as a set of weighted samples drawn from the posterior. In this paper, we emphasize nested sampling and all classes that are directly connected to it. Additionally, we present the fitters, which fit the data by the least-squares method or the maximum likelihood method. They can also calculate the Bayesian evidence as a Gaussian approximation. We will discuss the architecture of the toolbox. Which classes are present, what is their function, how they are related and implementational details where it gets complicated.

Authors 2

1. D. J. M. Kester Aachen SRON Netherlands Institute for Space Research

   Space Research Organisation Netherlands

   Affiliation as printed

   SRON Netherlands Institute for Space Research , Postbus 800 , 9700AV Groningen , The Netherlands

2. Michael Mueller Aachen Leiden Observatory SRON Netherlands Institute for Space Research

   Leiden University · Leiden Observatory · Space Research Organisation Netherlands

   Affiliation as printed

   Leiden Observatory , Leiden University , P.O. Box 9513 , 2300 RA Leiden , The Netherlands

   SRON Netherlands Institute for Space Research , Postbus 800 , 9700AV Groningen , The Netherlands