Bayesian parameter estimation for discrete data spectra

[摘要] ENGLISH ABSTRACT : Discrete spectra are ubiquitous in physics; for example nuclear physics, laser physics andexperimental high energy physics measure integer counts in the form of particles in dependenceof angle, wavelength, energy etc. Bayesian parameter estimation ( tting a functionwith free parameters to the data) is a sophisticated framework which can handle cases ofsparse data as well as input of pertinent background information into the data analysis inthe form of a prior probability. Bayesian comparison of competing models and functionstakes into account all possible parameter values rather than just the bestt values. Werstreview the general statistical basis of data analysis, focusing in particular on the Poisson,Negative Binomial and associated distributions. After introducing the conceptual shift andbasic relations of the Bayesian approach, we show how these distributions can be combinedwith arbitrary model functions and data counts to yield two general discrete likelihoods.While we keep an eye on the asymptotic behaviour as useful analytical checks, we then introduceand review the theoretical basis for Markov Chain Monte Carlo numerical methodsand show how these are applied in practice in the Metropolis-Hastings and Nested Samplingalgorithms. We proceed to apply these to a number of simple situations based on simulationof a background plus two or three Gaussian peaks with both Poisson and Negative Binomiallikelihoods, and discuss how to select models based on numerical outputs.

[发布机构] Stellenbosch University