Thesis (PhD)--Stellenbosch University, 2014. / 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. / AFRIKAANSE OPSOMMING: Ons ondersoek the prosedure om waarskynlikhede aan logiese stellings toe te ken. Die
eenvoudigste geval is die van ewewig-statistiese meganika en die ooreenkomstige fundamentele
aanname van ewekansige toestande. Hera
eiding van die standaard formulering
lei ons tot die bevraagtekening van die aanname van logiese onafhanklikheid en spesi ek
die onmoontlikheid van opdatering van waarskynlikheid wanneer data beskikbaar raak.
Gevolglik vervang ons die aanname van logiese onafhanklikheid met De Finetti se aanname
van omruilbaarheid. Om die ooreenkomstige voorstelling stellings te gebruik moet ons a
priori verdelings konstrueer vir 'n paar algemene parameter-ruimtes. Ons stel voor dat
stabiliteits-eienskappe gebruik moet word om geskikte a priori distribusies te identi seer.
Die kombinase van omruilbare aanneemlikheids funksies en die ooreenkomstige a priori
verdelings lei ons tot nuwe toekennings van getuienis-verdelings. Hierdie nuwe getuienesverdelings
is n veralgemening van Shannon se entropie na ander entropie-maatstawwe. Die
doel van hierdie entropie formalismes is om 'n raamwerk vir modelkonstruksie te verskaf.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/86545 |
| Date | 04 1900 |
| Creators | De Kock, Michiel Burger |
| Contributors | Eggers, H. C., Stellenbosch University. Faculty of Science. Dept. of Physics. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | English |
| Type | Thesis |
| Format | xi, 140 p. |
| Rights | Stellenbosch University |
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