Browsing by Author "Wang, Li"

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    Bayesian parameter estimation for discrete data spectra
    (Stellenbosch : Stellenbosch University, 2017-12) Wang, Li; Eggers, H. C.; Stellenbosch University. Faculty of Science. Dept. of Physics.
    ENGLISH ABSTRACT : Discrete spectra are ubiquitous in physics; for example nuclear physics, laser physics and experimental high energy physics measure integer counts in the form of particles in dependence of angle, wavelength, energy etc. Bayesian parameter estimation ( tting a function with free parameters to the data) is a sophisticated framework which can handle cases of sparse data as well as input of pertinent background information into the data analysis in the form of a prior probability. Bayesian comparison of competing models and functions takes into account all possible parameter values rather than just the best t values. We rst review the general statistical basis of data analysis, focusing in particular on the Poisson, Negative Binomial and associated distributions. After introducing the conceptual shift and basic relations of the Bayesian approach, we show how these distributions can be combined with 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 introduce and review the theoretical basis for Markov Chain Monte Carlo numerical methods and show how these are applied in practice in the Metropolis-Hastings and Nested Sampling algorithms. We proceed to apply these to a number of simple situations based on simulation of a background plus two or three Gaussian peaks with both Poisson and Negative Binomial likelihoods, and discuss how to select models based on numerical outputs.