{"id":{"repo_id":"vcu","oai_identifier":"oai:scholarscompass.vcu.edu:etd-1074"},"canonical_url":"https://search.dev.ndltd.org/etd/vcu/oai:scholarscompass.vcu.edu:etd-1074","repository":{"repo_id":"vcu","name":"Virginia Commonwealth University","base_url":"https://scholarscompass.vcu.edu/do/oai/"},"display":{"title":"Multivariate Steepest Ascent Using Bayesian Reliability","abstract":"The path of steepest ascent can used to optimize a response in an experiment, but problems can occur with multiple responses. Past approaches to this issue such as Del Castillo’s overlap of confidence cones and Mee and Xiao’s Pareto Optimality, have not considered the correlations of the responses or parameter uncertainty. We propose a new method using the Bayesian reliability to calculate this direction. We utilize this method with four examples: a 2 factor, 2-response experiment where the paths of steepest ascent are similar, ensuring our results match Del Castillo’s and Mee and Xiao’s; a 2 factor, 2-response experiment with disparate paths of steepest ascent illustrating the importance of the Bayesian reliability; two simulation examples, showing parameter uncertainty is considered; and a 5 factor, 2-response experiment proving this method is not dimensional limited. With a Bayesian reliable point, a direction in multivariate steepest ascent can be found.","abstract_html":"The path of steepest ascent can used to optimize a response in an experiment, but problems can occur with multiple responses. Past approaches to this issue such as Del Castillo’s overlap of confidence cones and Mee and Xiao’s Pareto Optimality, have not considered the correlations of the responses or parameter uncertainty. We propose a new method using the Bayesian reliability to calculate this direction. We utilize this method with four examples: a 2 factor, 2-response experiment where the paths of steepest ascent are similar, ensuring our results match Del Castillo’s and Mee and Xiao’s; a 2 factor, 2-response experiment with disparate paths of steepest ascent illustrating the importance of the Bayesian reliability; two simulation examples, showing parameter uncertainty is considered; and a 5 factor, 2-response experiment proving this method is not dimensional limited. With a Bayesian reliable point, a direction in multivariate steepest ascent can be found.","abstract_has_math":false,"creators":["Fuerte, Jeffrey"],"institution":null,"degree_name":"Master of Science","degree_level":"Thesis","degree_discipline":"Mathematical Sciences","degree_department":null,"school":null,"contributors":["David Edwards"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010-05-04T07:00:00Z","date_published":"2010-05-04T07:00:00Z","updated_at":"2026-07-24T05:53:18Z","subjects":["Multivariate Steepest Ascent","Bayesian Reliability","Physical Sciences and Mathematics"],"languages":[],"rights":["© The Author"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarscompass.vcu.edu/etd/75"],"render_values":[{"text":"https://scholarscompass.vcu.edu/etd/75","href":"https://scholarscompass.vcu.edu/etd/75","code":true}]}]},"links":{"outbound_url":"https://doi.org/10.25772/6QS3-E016","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["David Edwards"]},{"key":"dc:creator","label":"Author","values":["Fuerte, Jeffrey"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2015-05-14T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Multivariate Steepest Ascent","Bayesian Reliability","Physical Sciences and Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["© The Author"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://doi.org/10.25772/6QS3-E016","https://scholarscompass.vcu.edu/etd/75"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The path of steepest ascent can used to optimize a response in an experiment, but problems can occur with multiple responses. Past approaches to this issue such as Del Castillo’s overlap of confidence cones and Mee and Xiao’s Pareto Optimality, have not considered the correlations of the responses or parameter uncertainty. We propose a new method using the Bayesian reliability to calculate this direction. We utilize this method with four examples: a 2 factor, 2-response experiment where the paths of steepest ascent are similar, ensuring our results match Del Castillo’s and Mee and Xiao’s; a 2 factor, 2-response experiment with disparate paths of steepest ascent illustrating the importance of the Bayesian reliability; two simulation examples, showing parameter uncertainty is considered; and a 5 factor, 2-response experiment proving this method is not dimensional limited. With a Bayesian reliable point, a direction in multivariate steepest ascent can be found."]},{"key":"dc:title","label":"Title","values":["Multivariate Steepest Ascent Using Bayesian Reliability"]}]}],"canonical_facts":{"dc:contributor":["David Edwards"],"dc:creator":["Fuerte, Jeffrey"],"dc:date.available":["2015-05-14T07:00:00Z"],"dc:description.abstract":["The path of steepest ascent can used to optimize a response in an experiment, but problems can occur with multiple responses. Past approaches to this issue such as Del Castillo’s overlap of confidence cones and Mee and Xiao’s Pareto Optimality, have not considered the correlations of the responses or parameter uncertainty. We propose a new method using the Bayesian reliability to calculate this direction. We utilize this method with four examples: a 2 factor, 2-response experiment where the paths of steepest ascent are similar, ensuring our results match Del Castillo’s and Mee and Xiao’s; a 2 factor, 2-response experiment with disparate paths of steepest ascent illustrating the importance of the Bayesian reliability; two simulation examples, showing parameter uncertainty is considered; and a 5 factor, 2-response experiment proving this method is not dimensional limited. With a Bayesian reliable point, a direction in multivariate steepest ascent can be found."],"dc:identifier":["https://doi.org/10.25772/6QS3-E016","https://scholarscompass.vcu.edu/etd/75"],"dc:rights":["© The Author"],"dc:subject":["Multivariate Steepest Ascent","Bayesian Reliability","Physical Sciences and Mathematics"],"dc:title":["Multivariate Steepest Ascent Using Bayesian Reliability"],"thesis:degree_discipline":["Mathematical Sciences"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Science"]},"updated_at":"2026-07-24T05:53:18Z"}