{"id":{"repo_id":"byu","oai_identifier":"oai:scholarsarchive.byu.edu:etd-2248"},"canonical_url":"https://search.dev.ndltd.org/etd/byu/oai:scholarsarchive.byu.edu:etd-2248","repository":{"repo_id":"byu","name":"Brigham Young University","base_url":"https://scholarsarchive.byu.edu/do/oai/"},"display":{"title":"Modeling Transition Probabilities for Loan States Using a Bayesian Hierarchical Model","abstract":"A Markov Chain model can be used to model loan defaults because loans move through delinquency states as the borrower fails to make monthly payments. The transition matrix contains in each location a probability that a borrower in a given state one month moves to the possible delinquency states the next month. In order to use this model, it is necessary to know the transition probabilities, which are unknown quantities. A Bayesian hierarchical model is postulated because there may not be sufficient data for some rare transition probabilities. Using a hierarchical model, similarities between types or families of loans can be taken advantage of to improve estimation, especially for those probabilities with little associated data. The transition probabilities are estimated using MCMC and the Metropolis-Hastings algorithm.","abstract_html":"A Markov Chain model can be used to model loan defaults because loans move through delinquency states as the borrower fails to make monthly payments. The transition matrix contains in each location a probability that a borrower in a given state one month moves to the possible delinquency states the next month. In order to use this model, it is necessary to know the transition probabilities, which are unknown quantities. A Bayesian hierarchical model is postulated because there may not be sufficient data for some rare transition probabilities. Using a hierarchical model, similarities between types or families of loans can be taken advantage of to improve estimation, especially for those probabilities with little associated data. The transition probabilities are estimated using MCMC and the Metropolis-Hastings algorithm.","abstract_has_math":false,"creators":["Monson, Rebecca Lee"],"institution":"Brigham Young University - Provo","degree_name":"MS","degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T01:29:03Z","subjects":["MCMC","Hierarchical Model","multinomial","Dirichlet","Statistics and Probability"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarsarchive.byu.edu/etd/1249","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Monson, Rebecca Lee"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2007-11-30T08:00:00Z"]},{"key":"dc:publisher","label":"Institution","values":["Brigham Young University - Provo"]},{"key":"dc:type","label":"Dc Type","values":["Selected Project"]},{"key":"thesis:degree_name","label":"Degree Name","values":["MS"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["MCMC","Hierarchical Model","multinomial","Dirichlet","Statistics and Probability"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarsarchive.byu.edu/etd/1249","https://scholarsarchive.byu.edu/context/etd/article/2248/viewcontent/ETD_CISOPTR_1253.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Physical and Mathematical Sciences; Statistics"]},{"key":"dc:description.abstract","label":"Abstract","values":["A Markov Chain model can be used to model loan defaults because loans move through delinquency states as the borrower fails to make monthly payments. The transition matrix contains in each location a probability that a borrower in a given state one month moves to the possible delinquency states the next month. In order to use this model, it is necessary to know the transition probabilities, which are unknown quantities. A Bayesian hierarchical model is postulated because there may not be sufficient data for some rare transition probabilities. Using a hierarchical model, similarities between types or families of loans can be taken advantage of to improve estimation, especially for those probabilities with little associated data. The transition probabilities are estimated using MCMC and the Metropolis-Hastings algorithm."]},{"key":"dc:format","label":"Dc Format","values":["application:pdf"]},{"key":"dc:source","label":"Dc Source","values":["Brigham Young University - Provo"]},{"key":"dc:title","label":"Title","values":["Modeling Transition Probabilities for Loan States Using a Bayesian Hierarchical Model"]}]}],"canonical_facts":{"dc:creator":["Monson, Rebecca Lee"],"dc:date":["2007-11-30T08:00:00Z"],"dc:description":["Physical and Mathematical Sciences; Statistics"],"dc:description.abstract":["A Markov Chain model can be used to model loan defaults because loans move through delinquency states as the borrower fails to make monthly payments. The transition matrix contains in each location a probability that a borrower in a given state one month moves to the possible delinquency states the next month. In order to use this model, it is necessary to know the transition probabilities, which are unknown quantities. A Bayesian hierarchical model is postulated because there may not be sufficient data for some rare transition probabilities. Using a hierarchical model, similarities between types or families of loans can be taken advantage of to improve estimation, especially for those probabilities with little associated data. The transition probabilities are estimated using MCMC and the Metropolis-Hastings algorithm."],"dc:format":["application:pdf"],"dc:identifier":["https://scholarsarchive.byu.edu/etd/1249","https://scholarsarchive.byu.edu/context/etd/article/2248/viewcontent/ETD_CISOPTR_1253.pdf"],"dc:language":["English"],"dc:publisher":["Brigham Young University - Provo"],"dc:source":["Brigham Young University - Provo"],"dc:subject":["MCMC","Hierarchical Model","multinomial","Dirichlet","Statistics and Probability"],"dc:title":["Modeling Transition Probabilities for Loan States Using a Bayesian Hierarchical Model"],"dc:type":["Selected Project"],"thesis:degree_name":["MS"]},"updated_at":"2026-07-24T01:29:03Z"}