{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/66463"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/66463","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Computability, inference and modeling in probabilistic programming","abstract":"We investigate the class of computable probability distributions and explore the fundamental limitations of using this class to describe and compute conditional distributions. In addition to proving the existence of noncomputable conditional distributions, and thus ruling out the possibility of generic probabilistic inference algorithms (even inefficient ones), we highlight some positive results showing that posterior inference is possible in the presence of additional structure like exchangeability and noise, both of which are common in Bayesian hierarchical modeling. This theoretical work bears on the development of probabilistic programming languages (which enable the specification of complex probabilistic models) and their implementations (which can be used to perform Bayesian reasoning). The probabilistic programming approach is particularly well suited for defining infinite-dimensional, recursively-defined stochastic processes of the sort used in nonparametric Bayesian statistics. We present a new construction of the Mondrian process as a partition-valued Markov process in continuous time, which can be viewed as placing a distribution on an infinite kd-tree data structure.","abstract_html":"We investigate the class of computable probability distributions and explore the fundamental limitations of using this class to describe and compute conditional distributions. In addition to proving the existence of noncomputable conditional distributions, and thus ruling out the possibility of generic probabilistic inference algorithms (even inefficient ones), we highlight some positive results showing that posterior inference is possible in the presence of additional structure like exchangeability and noise, both of which are common in Bayesian hierarchical modeling. This theoretical work bears on the development of probabilistic programming languages (which enable the specification of complex probabilistic models) and their implementations (which can be used to perform Bayesian reasoning). The probabilistic programming approach is particularly well suited for defining infinite-dimensional, recursively-defined stochastic processes of the sort used in nonparametric Bayesian statistics. We present a new construction of the Mondrian process as a partition-valued Markov process in continuous time, which can be viewed as placing a distribution on an infinite kd-tree data structure.","abstract_has_math":false,"creators":["Roy, Daniel Murphy"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.","school":null,"contributors":[],"advisors":["Leslie P. Kaelbling."],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011","date_published":"2011","updated_at":"2026-07-22T22:21:51Z","subjects":["Electrical Engineering and Computer Science."],"languages":["eng"],"rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."],"rights_urls":["http://dspace.mit.edu/handle/1721.1/7582"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/1721.1/66463","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Leslie P. Kaelbling."]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science."]},{"key":"dc:contributor.other","label":"Dc Contributor Other","values":["Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science."]},{"key":"dc:creator","label":"Author","values":["Roy, Daniel Murphy"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2011-10-17T21:28:58Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2011-10-17T21:28:58Z"]},{"key":"dc:date.issued","label":"Date","values":["2011"]},{"key":"dc:publisher","label":"Institution","values":["Massachusetts Institute of Technology"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Electrical Engineering and Computer Science."]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://dspace.mit.edu/handle/1721.1/7582"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1721.1/66463"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2011.","Cataloged from PDF version of thesis.","Includes bibliographical references (p. 135-144)."]},{"key":"dc:description.abstract","label":"Abstract","values":["We investigate the class of computable probability distributions and explore the fundamental limitations of using this class to describe and compute conditional distributions. In addition to proving the existence of noncomputable conditional distributions, and thus ruling out the possibility of generic probabilistic inference algorithms (even inefficient ones), we highlight some positive results showing that posterior inference is possible in the presence of additional structure like exchangeability and noise, both of which are common in Bayesian hierarchical modeling. This theoretical work bears on the development of probabilistic programming languages (which enable the specification of complex probabilistic models) and their implementations (which can be used to perform Bayesian reasoning). The probabilistic programming approach is particularly well suited for defining infinite-dimensional, recursively-defined stochastic processes of the sort used in nonparametric Bayesian statistics. We present a new construction of the Mondrian process as a partition-valued Markov process in continuous time, which can be viewed as placing a distribution on an infinite kd-tree data structure."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph.D."]},{"key":"dc:title","label":"Title","values":["Computability, inference and modeling in probabilistic programming"]}]}],"canonical_facts":{"dc:contributor.advisor":["Leslie P. Kaelbling."],"dc:contributor.department":["Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science."],"dc:contributor.other":["Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science."],"dc:creator":["Roy, Daniel Murphy"],"dc:date.accessioned":["2011-10-17T21:28:58Z"],"dc:date.available":["2011-10-17T21:28:58Z"],"dc:date.issued":["2011"],"dc:description":["Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2011.","Cataloged from PDF version of thesis.","Includes bibliographical references (p. 135-144)."],"dc:description.abstract":["We investigate the class of computable probability distributions and explore the fundamental limitations of using this class to describe and compute conditional distributions. In addition to proving the existence of noncomputable conditional distributions, and thus ruling out the possibility of generic probabilistic inference algorithms (even inefficient ones), we highlight some positive results showing that posterior inference is possible in the presence of additional structure like exchangeability and noise, both of which are common in Bayesian hierarchical modeling. This theoretical work bears on the development of probabilistic programming languages (which enable the specification of complex probabilistic models) and their implementations (which can be used to perform Bayesian reasoning). The probabilistic programming approach is particularly well suited for defining infinite-dimensional, recursively-defined stochastic processes of the sort used in nonparametric Bayesian statistics. We present a new construction of the Mondrian process as a partition-valued Markov process in continuous time, which can be viewed as placing a distribution on an infinite kd-tree data structure."],"dc:description.degree":["Ph.D."],"dc:identifier.uri":["http://hdl.handle.net/1721.1/66463"],"dc:language.iso":["eng"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."],"dc:rights.uri":["http://dspace.mit.edu/handle/1721.1/7582"],"dc:subject":["Electrical Engineering and Computer Science."],"dc:title":["Computability, inference and modeling in probabilistic programming"],"dc:type":["Thesis"]},"updated_at":"2026-07-22T22:21:51Z"}