In this thesis, we use the model-based clustering procedure to cluster fifteen Zernike coefficients into groups. Quantile regressions are considered to describe the relationship between Zernike coefficients and pupil size. We employ Gibbs sampler and adaptive rejection Metropolis sampling to infer the parameters for each cluster. Bayesian information criterion (BIC) combined with a measure of uncertainty are used to determine the number of clusters. A comparison of likelihoods between the unclustered and the clustered Zernike coefficients is implemented to determine the quantile at which population heterogeneity is the most significant. We illustrate the performance of the proposed method using both simulated and real data sets. In the ophthalmology data application, at quantile =0.65, the population are most heterogeneous and divided into two clusters.
","abstract_html":"<p>In this thesis, we use the model-based clustering procedure to cluster fifteen Zernike coefficients into groups. Quantile regressions are considered to describe the relationship between Zernike coefficients and pupil size. We employ Gibbs sampler and adaptive rejection Metropolis sampling to infer the parameters for each cluster. Bayesian information criterion (BIC) combined with a measure of uncertainty are used to determine the number of clusters. A comparison of likelihoods between the unclustered and the clustered Zernike coefficients is implemented to determine the quantile at which population heterogeneity is the most significant. We illustrate the performance of the proposed method using both simulated and real data sets. In the ophthalmology data application, at quantile =0.65, the population are most heterogeneous and divided into two clusters.</p>","abstract_has_math":false,"creators":["Tong, Xin"],"institution":null,"degree_name":"M.S.P.H.","degree_level":"Campus Access Thesis","degree_discipline":"Epidemiology and Biostatistics","degree_department":null,"school":null,"contributors":["Hongmei Zhang"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-01-01T08:00:00Z","date_published":"2011-01-01T08:00:00Z","updated_at":"2026-07-24T04:37:21Z","subjects":["Biostatistics","Physical Sciences and Mathematics","Statistics and Probability"],"languages":[],"rights":["© 2011, Xin Tong"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarcommons.sc.edu/etd/557","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Hongmei Zhang"]},{"key":"dc:creator","label":"Author","values":["Tong, Xin"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Epidemiology and Biostatistics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Campus Access Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S.P.H."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Biostatistics","Physical Sciences and Mathematics","Statistics and Probability"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["© 2011, Xin Tong"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarcommons.sc.edu/etd/557"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis, we use the model-based clustering procedure to cluster fifteen Zernike coefficients into groups. Quantile regressions are considered to describe the relationship between Zernike coefficients and pupil size. We employ Gibbs sampler and adaptive rejection Metropolis sampling to infer the parameters for each cluster. Bayesian information criterion (BIC) combined with a measure of uncertainty are used to determine the number of clusters. A comparison of likelihoods between the unclustered and the clustered Zernike coefficients is implemented to determine the quantile at which population heterogeneity is the most significant. We illustrate the performance of the proposed method using both simulated and real data sets. In the ophthalmology data application, at quantile =0.65, the population are most heterogeneous and divided into two clusters.
"]},{"key":"dc:title","label":"Title","values":["Clustering Analysis of Zernike Coefficients Through Quantile Regression"]}]}],"canonical_facts":{"dc:contributor":["Hongmei Zhang"],"dc:creator":["Tong, Xin"],"dc:description.abstract":["In this thesis, we use the model-based clustering procedure to cluster fifteen Zernike coefficients into groups. Quantile regressions are considered to describe the relationship between Zernike coefficients and pupil size. We employ Gibbs sampler and adaptive rejection Metropolis sampling to infer the parameters for each cluster. Bayesian information criterion (BIC) combined with a measure of uncertainty are used to determine the number of clusters. A comparison of likelihoods between the unclustered and the clustered Zernike coefficients is implemented to determine the quantile at which population heterogeneity is the most significant. We illustrate the performance of the proposed method using both simulated and real data sets. In the ophthalmology data application, at quantile =0.65, the population are most heterogeneous and divided into two clusters.
"],"dc:identifier":["https://scholarcommons.sc.edu/etd/557"],"dc:rights":["© 2011, Xin Tong"],"dc:subject":["Biostatistics","Physical Sciences and Mathematics","Statistics and Probability"],"dc:title":["Clustering Analysis of Zernike Coefficients Through Quantile Regression"],"thesis:degree_discipline":["Epidemiology and Biostatistics"],"thesis:degree_level":["Campus Access Thesis"],"thesis:degree_name":["M.S.P.H."]},"updated_at":"2026-07-24T04:37:21Z"}