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From stable priors to maximum Bayesian evidence via a generalised rule of succession
Thesis (PhD)--Stellenbosch University, 2014.
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| Format: | Thesis |
| Language: | en_ZA |
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Stellenbosch : Stellenbosch University
2014
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| _version_ | 1867614117471191040 |
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| access_status_str | Open Access |
| author | De Kock, Michiel Burger |
| author2 | Eggers, H. C. |
| author_browse | De Kock, Michiel Burger Eggers, H. C. |
| author_facet | Eggers, H. C. De Kock, Michiel Burger |
| author_sort | De Kock, Michiel Burger |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (PhD)--Stellenbosch University, 2014. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/86545 |
| institution | Stellenbosch University (South Africa) |
| language | en_ZA |
| last_indexed | 2026-06-10T12:46:56.603Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2014 |
| publishDateRange | 2014 |
| publishDateSort | 2014 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/86545 From stable priors to maximum Bayesian evidence via a generalised rule of succession De Kock, Michiel Burger Eggers, H. C. Stellenbosch University. Faculty of Science. Dept. of Physics. Bayesian analysis Statistical physics Entropy UCTD Dissertations -- Physics Theses -- Physics 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. Doctoral 2014-04-16T17:29:56Z 2014-04-16T17:29:56Z 2014-04 Thesis http://hdl.handle.net/10019.1/86545 en_ZA Stellenbosch University xi, 140 p. application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Bayesian analysis Statistical physics Entropy UCTD Dissertations -- Physics Theses -- Physics De Kock, Michiel Burger From stable priors to maximum Bayesian evidence via a generalised rule of succession |
| title | From stable priors to maximum Bayesian evidence via a generalised rule of succession |
| title_full | From stable priors to maximum Bayesian evidence via a generalised rule of succession |
| title_fullStr | From stable priors to maximum Bayesian evidence via a generalised rule of succession |
| title_full_unstemmed | From stable priors to maximum Bayesian evidence via a generalised rule of succession |
| title_short | From stable priors to maximum Bayesian evidence via a generalised rule of succession |
| title_sort | from stable priors to maximum bayesian evidence via a generalised rule of succession |
| topic | Bayesian analysis Statistical physics Entropy UCTD Dissertations -- Physics Theses -- Physics |
| url | http://hdl.handle.net/10019.1/86545 |
| work_keys_str_mv | AT dekockmichielburger fromstablepriorstomaximumbayesianevidenceviaageneralisedruleofsuccession |