{"id":{"repo_id":"wustl","oai_identifier":"oai:openscholarship.wustl.edu:art_sci_etds-1458"},"canonical_url":"https://search.dev.ndltd.org/etd/wustl/oai:openscholarship.wustl.edu:art_sci_etds-1458","repository":{"repo_id":"wustl","name":"Washington University in St. Louis","base_url":"https://openscholarship.wustl.edu/do/oai/"},"display":{"title":"Nonparametric Bayesian Quantile Regression via Dirichlet Process Mixture Models","abstract":"We propose new nonparametric Bayesian approaches to quantile regression usingDirichlet process mixture (DPM) models. All the existing quantile regression methodsbased on DPMs require the kernel density to satisfy the quantile constraint, hence thekernel densities are themselves usually in the form of mixtures. One innovation of ourapproaches is that we impose no constraint on the kernel, thus a wide range of densitiescan be chosen as the kernels of the DPM model. The quantile constraint is satisfied by apost-processing of the DPM by a suitable location shift. As a result, our proposed modelsuse simpler kernels and yet possess great flexibility by mixing over both the locationparameter and the scale parameter. The posterior consistency of our proposed model isstudied carefully. And Markov chain Monte Carlo algorithms are provided for posteriorinference. The performance of our approaches is evaluated using simulated data and realdata. Moreover, we are able to incorporate random effects into our models such that ourapproaches can be extended to handle longitudinal data.","abstract_html":"We propose new nonparametric Bayesian approaches to quantile regression usingDirichlet process mixture (DPM) models. All the existing quantile regression methodsbased on DPMs require the kernel density to satisfy the quantile constraint, hence thekernel densities are themselves usually in the form of mixtures. One innovation of ourapproaches is that we impose no constraint on the kernel, thus a wide range of densitiescan be chosen as the kernels of the DPM model. The quantile constraint is satisfied by apost-processing of the DPM by a suitable location shift. As a result, our proposed modelsuse simpler kernels and yet possess great flexibility by mixing over both the locationparameter and the scale parameter. The posterior consistency of our proposed model isstudied carefully. And Markov chain Monte Carlo algorithms are provided for posteriorinference. The performance of our approaches is evaluated using simulated data and realdata. Moreover, we are able to incorporate random effects into our models such that ourapproaches can be extended to handle longitudinal data.","abstract_has_math":false,"creators":["Chang, Chao"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Nan Lin","Siddhartha Chib, Jimin Ding, Todd Kuffner, Mladen Victor Wickerhauser"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-05-15T07:00:00Z","date_published":"2015-05-15T07:00:00Z","updated_at":"2026-07-24T06:12:08Z","subjects":["Dirichlet Process Mixture","Nonparametric Bayesian","Posterior Consistency","Quantile Regression","Mathematics"],"languages":["English (en)"],"rights":["I have not registered my thesis with the U.S. Copyright Office, and do not intend to."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["https://openscholarship.wustl.edu/art_sci_etds/458"],"render_values":[{"text":"https://openscholarship.wustl.edu/art_sci_etds/458","href":"https://openscholarship.wustl.edu/art_sci_etds/458","code":true}]}]},"links":{"outbound_url":"https://doi.org/10.7936/K7TQ5ZPC","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Nan Lin","Siddhartha Chib, Jimin Ding, Todd Kuffner, Mladen Victor Wickerhauser"]},{"key":"dc:creator","label":"Author","values":["Chang, Chao"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2015-10-27T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics","Graduate School of Arts and Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Dirichlet Process Mixture","Nonparametric Bayesian","Posterior Consistency","Quantile Regression","Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English (en)"]},{"key":"dc:rights","label":"Dc Rights","values":["I have not registered my thesis with the U.S. Copyright Office, and do not intend to."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://doi.org/10.7936/K7TQ5ZPC","https://openscholarship.wustl.edu/art_sci_etds/458"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Permanent URL: https://doi.org/10.7936/K7TQ5ZPC"]},{"key":"dc:description.abstract","label":"Abstract","values":["We propose new nonparametric Bayesian approaches to quantile regression usingDirichlet process mixture (DPM) models. All the existing quantile regression methodsbased on DPMs require the kernel density to satisfy the quantile constraint, hence thekernel densities are themselves usually in the form of mixtures. One innovation of ourapproaches is that we impose no constraint on the kernel, thus a wide range of densitiescan be chosen as the kernels of the DPM model. The quantile constraint is satisfied by apost-processing of the DPM by a suitable location shift. As a result, our proposed modelsuse simpler kernels and yet possess great flexibility by mixing over both the locationparameter and the scale parameter. The posterior consistency of our proposed model isstudied carefully. And Markov chain Monte Carlo algorithms are provided for posteriorinference. The performance of our approaches is evaluated using simulated data and realdata. Moreover, we are able to incorporate random effects into our models such that ourapproaches can be extended to handle longitudinal data."]},{"key":"dc:title","label":"Title","values":["Nonparametric Bayesian Quantile Regression via Dirichlet Process Mixture Models"]}]}],"canonical_facts":{"dc:contributor":["Nan Lin","Siddhartha Chib, Jimin Ding, Todd Kuffner, Mladen Victor Wickerhauser"],"dc:creator":["Chang, Chao"],"dc:date.available":["2015-10-27T07:00:00Z"],"dc:description":["Permanent URL: https://doi.org/10.7936/K7TQ5ZPC"],"dc:description.abstract":["We propose new nonparametric Bayesian approaches to quantile regression usingDirichlet process mixture (DPM) models. All the existing quantile regression methodsbased on DPMs require the kernel density to satisfy the quantile constraint, hence thekernel densities are themselves usually in the form of mixtures. One innovation of ourapproaches is that we impose no constraint on the kernel, thus a wide range of densitiescan be chosen as the kernels of the DPM model. The quantile constraint is satisfied by apost-processing of the DPM by a suitable location shift. As a result, our proposed modelsuse simpler kernels and yet possess great flexibility by mixing over both the locationparameter and the scale parameter. The posterior consistency of our proposed model isstudied carefully. And Markov chain Monte Carlo algorithms are provided for posteriorinference. The performance of our approaches is evaluated using simulated data and realdata. Moreover, we are able to incorporate random effects into our models such that ourapproaches can be extended to handle longitudinal data."],"dc:identifier":["https://doi.org/10.7936/K7TQ5ZPC","https://openscholarship.wustl.edu/art_sci_etds/458"],"dc:language":["English (en)"],"dc:rights":["I have not registered my thesis with the U.S. Copyright Office, and do not intend to."],"dc:subject":["Dirichlet Process Mixture","Nonparametric Bayesian","Posterior Consistency","Quantile Regression","Mathematics"],"dc:title":["Nonparametric Bayesian Quantile Regression via Dirichlet Process Mixture Models"],"thesis:degree_discipline":["Mathematics","Graduate School of Arts and Sciences"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T06:12:08Z"}