Doctoral Degrees (Physics)

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From stable priors to maximum Bayesian evidence via a generalised rule of succession
(Stellenbosch : Stellenbosch University, 2014-04) De Kock, Michiel Burger; Eggers, H. C.; Stellenbosch University. Faculty of Science. Dept. of Physics.
ENGLISH ABSTRACT: We investigate the procedure of assigning probabilities to logical statements. The simplest case is that of equilibrium statistical mechanics and its fundamental assumption of equally likely states. Rederiving the formulation led us to question the assumption of logical independence inherent to the construction and speci cally its inability to update probability when data becomes available. Consequently we replace the assumption of logical independence with De Finetti's concept of exchangeability. To use the corresponding representation theorems of De Finetti requires us to assign prior distributions for some general parameter spaces. We propose the use of stability properties to identify suitable prior distributions. The combination of exchangeable likelihoods and corresponding prior distributions results in more general evidence distribution assignments. These new evidence assignments generalise the Shannon entropy to other entropy measures. The goal of these entropy formulations is to provide a general framework for constructing models.