{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/106468"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/106468","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Statistical methods for binomial and Gaussian sequences","abstract":"We propose new methods and frameworks for approaching three different statistical sequence problems. The first is a tree-based computational method for calculating the Poisson Binomial distribution function, which is the distribution of a sum of independent but not identically distributed Bernoulli random variables. Our proposed scheme is shown to be the fastest available method for exact computation of the distribution function. The second problem we study is community detection and link probability estimation in network data. We propose a novel Random Forest methodology adapted to network data in order to approach these problems, which utilizes the Random Forest to construct a kernel encoding similarities between network vertices. To our knowledge, this is the first instance in which Random Forests have been applied to these problems. Unlike standard Random Forest approaches, these methods are fully unsupervised. The efficacy of the proposed methods is demonstrated via extensive simulations, and they are shown to achieve state of the art performance. Finally, we present a new approach for tackling the classical Normal means sequence problem, which takes a modeling perspective. This new perspective allows for the straightforward development of new estimators, which unlike most currently available estimators, are able to incorporate covariate information. Due to the perspective we take, we are further able to perform inference on parameters in the model. We provide several theoretical results that show our approach yields estimators with favorable properties. We also demonstrate the effectiveness of the proposed approach through a comprehensive simulation study.","abstract_html":"We propose new methods and frameworks for approaching three different statistical sequence problems. The first is a tree-based computational method for calculating the Poisson Binomial distribution function, which is the distribution of a sum of independent but not identically distributed Bernoulli random variables. Our proposed scheme is shown to be the fastest available method for exact computation of the distribution function. The second problem we study is community detection and link probability estimation in network data. We propose a novel Random Forest methodology adapted to network data in order to approach these problems, which utilizes the Random Forest to construct a kernel encoding similarities between network vertices. To our knowledge, this is the first instance in which Random Forests have been applied to these problems. Unlike standard Random Forest approaches, these methods are fully unsupervised. The efficacy of the proposed methods is demonstrated via extensive simulations, and they are shown to achieve state of the art performance. Finally, we present a new approach for tackling the classical Normal means sequence problem, which takes a modeling perspective. This new perspective allows for the straightforward development of new estimators, which unlike most currently available estimators, are able to incorporate covariate information. Due to the perspective we take, we are further able to perform inference on parameters in the model. We provide several theoretical results that show our approach yields estimators with favorable properties. We also demonstrate the effectiveness of the proposed approach through a comprehensive simulation study.","abstract_has_math":false,"creators":["Biscarri, William"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Statistics","degree_department":null,"school":null,"contributors":["Zhao, Sihai Dave","Brunner, Robert","Zhu, Ruoqing","Chen, Yuguo"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020-03-02T22:38:49Z","date_published":"2020-03-02T22:38:49Z","updated_at":"2026-07-22T22:24:47Z","subjects":["Random Forest","James Stein","Poisson Binomial","Compound Decision Theory","Empirical Bayes","Community Detection"],"languages":["en"],"rights":["Copyright 2019 William Dionis Biscarri"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/106468","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Zhao, Sihai Dave","Brunner, Robert","Zhu, Ruoqing","Chen, Yuguo"]},{"key":"dc:creator","label":"Author","values":["Biscarri, William"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2020-03-02T22:38:49Z","2022-03-03T10:15:25Z","2019-12-03","2019-12"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Statistics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Random Forest","James Stein","Poisson Binomial","Compound Decision Theory","Empirical Bayes","Community Detection"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2019 William Dionis Biscarri"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/106468"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["We propose new methods and frameworks for approaching three different statistical sequence problems. The first is a tree-based computational method for calculating the Poisson Binomial distribution function, which is the distribution of a sum of independent but not identically distributed Bernoulli random variables. Our proposed scheme is shown to be the fastest available method for exact computation of the distribution function. The second problem we study is community detection and link probability estimation in network data. We propose a novel Random Forest methodology adapted to network data in order to approach these problems, which utilizes the Random Forest to construct a kernel encoding similarities between network vertices. To our knowledge, this is the first instance in which Random Forests have been applied to these problems. Unlike standard Random Forest approaches, these methods are fully unsupervised. The efficacy of the proposed methods is demonstrated via extensive simulations, and they are shown to achieve state of the art performance. Finally, we present a new approach for tackling the classical Normal means sequence problem, which takes a modeling perspective. This new perspective allows for the straightforward development of new estimators, which unlike most currently available estimators, are able to incorporate covariate information. Due to the perspective we take, we are further able to perform inference on parameters in the model. We provide several theoretical results that show our approach yields estimators with favorable properties. We also demonstrate the effectiveness of the proposed approach through a comprehensive simulation study.","Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2021-12-01","The student, William Biscarri, accepted the attached license on 2019-11-30 at 17:28.","The student, William Biscarri, submitted this Dissertation for approval on 2019-11-30 at 17:36.","This Dissertation was approved for publication on 2019-12-03 at 10:38.","DSpace SAF Submission Ingestion Package generated from Vireo submission #14641 on 2020-02-28 at 17:37:05","Made available in DSpace on 2020-03-02T22:38:49Z (GMT). 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The first is a tree-based computational method for calculating the Poisson Binomial distribution function, which is the distribution of a sum of independent but not identically distributed Bernoulli random variables. Our proposed scheme is shown to be the fastest available method for exact computation of the distribution function. The second problem we study is community detection and link probability estimation in network data. We propose a novel Random Forest methodology adapted to network data in order to approach these problems, which utilizes the Random Forest to construct a kernel encoding similarities between network vertices. To our knowledge, this is the first instance in which Random Forests have been applied to these problems. Unlike standard Random Forest approaches, these methods are fully unsupervised. The efficacy of the proposed methods is demonstrated via extensive simulations, and they are shown to achieve state of the art performance. Finally, we present a new approach for tackling the classical Normal means sequence problem, which takes a modeling perspective. This new perspective allows for the straightforward development of new estimators, which unlike most currently available estimators, are able to incorporate covariate information. Due to the perspective we take, we are further able to perform inference on parameters in the model. We provide several theoretical results that show our approach yields estimators with favorable properties. We also demonstrate the effectiveness of the proposed approach through a comprehensive simulation study.","Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2021-12-01","The student, William Biscarri, accepted the attached license on 2019-11-30 at 17:28.","The student, William Biscarri, submitted this Dissertation for approval on 2019-11-30 at 17:36.","This Dissertation was approved for publication on 2019-12-03 at 10:38.","DSpace SAF Submission Ingestion Package generated from Vireo submission #14641 on 2020-02-28 at 17:37:05","Made available in DSpace on 2020-03-02T22:38:49Z (GMT). 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