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Advanced computing methods for statistical inference

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TitleInfo
Title
Advanced computing methods for statistical inference
Name (type = personal)
NamePart (type = family)
Thornton
NamePart (type = given)
Suzanne
NamePart (type = date)
1991-
DisplayForm
Suzanne Thornton
Role
RoleTerm (authority = RULIB)
author
Name (type = personal)
NamePart (type = family)
Xie
NamePart (type = given)
Min-ge
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Min-ge Xie
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
chair
Name (type = corporate)
NamePart
Rutgers University
Role
RoleTerm (authority = RULIB)
degree grantor
Name (type = corporate)
NamePart
School of Graduate Studies
Role
RoleTerm (authority = RULIB)
school
TypeOfResource
Text
Genre (authority = marcgt)
theses
OriginInfo
DateCreated (encoding = w3cdtf); (keyDate = yes); (qualifier = exact)
2019
DateOther (encoding = w3cdtf); (qualifier = exact); (type = degree)
2019-10
Language
LanguageTerm (authority = ISO 639-3:2007); (type = text)
English
Abstract (type = abstract)
In this thesis, we provide some new and interesting solutions to problems of computational inference. In particular, the two problems we address are (1) How to obtain valid confidence sets for parameters from models with no tractable likelihood function and (2) How to obtain valid exact confidence sets for the odds ratio when the signal is very difficult to detect. Our approach to solving these problems is to develop algorithmic procedures that result in confidence distributions for the parameters of interest. A confidence distribution can be thought of as a frequentist analog to a Bayesian posterior. It is a distribution estimate for a parameter of interest that provides inferential results
with respect to the Repeated Sampling Principle.

1. Most likelihood-free computational methods for statistical inference are performed under a Bayesian paradigm, even though they are driven by the need for inferential results in instances where the likelihood principle may fail. We develop a frequentist computational method to apply in situations where one has an intractable likelihood and instead rely on the Repeated Sampling Principle to justify our inferential results. Our method expands the applications of approximate Bayesian computing methods from and permits faster computational speed by eliminating the need for any prior information. Rather than attempting to work within a Bayesian framework without a tractable likelihood function, our method creates a special type of estimate, a confidence distribution, for the parameter of interest.

2. Establishing drug safety entails detecting relationships between treatments and rare, but adverse, events. For a 2x2 contingency tables of drug treatment and adverse events, this means that we are interested in inference for an odds ratio with a weak signal. In these situations, we will encounter very few adverse events, even if the number of patients under study is large. We develop a frequentist computational method for inference on sparse contingency tables that does not rely on large sample assumptions. Our method works under the assumption that one margin is fixed, enabling us to compare the observed data to simulated data through a data generating equation and a modied statistic. We make use of a stabilization parameter which allows us to consider smaller potential parameter values even if we have a zero observation in the data. This stabilization parameter makes our method distinct from the standard tail method approach. We show that our method can out-perform the overly-conservative existing exact methods and a Bayesian method.

In both of these problems, the algorithmic approaches we propose attempt to capture the sample variability using a known random variable connected to the data through a data-generating equation. In order to validate the inferential results within a frequentist framework, the algorithmic approaches to both of the above problems work by producing a specific type of estimator, a confidence distribution, for the unknown parameter. We think these two problems illustrate the rich possibilities for incorporating confidence distribution theory into the world of statistical computing.
Subject (authority = RUETD)
Topic
Statistics and Biostatistics
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
Identifier
ETD_10128
PhysicalDescription
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application/pdf
InternetMediaType
text/xml
Extent
1 online resource (vii, 67 pages) : illustrations
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
Subject (authority = local)
Topic
Bayesian inference
Subject (authority = LCSH)
Topic
Bayesian statistical decision theory
Subject (authority = LCSH)
Topic
Mathematical statistics
RelatedItem (type = host)
TitleInfo
Title
School of Graduate Studies Electronic Theses and Dissertations
Identifier (type = local)
rucore10001600001
Location
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NjNbRU
Identifier (type = doi)
doi:10.7282/t3-mveq-wk31
Genre (authority = ExL-Esploro)
ETD doctoral
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Rights

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The author owns the copyright to this work.
RightsHolder (type = personal)
Name
FamilyName
Thornton
GivenName
Suzanne
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime (encoding = w3cdtf); (qualifier = exact); (point = start)
2019-07-15 11:08:58
AssociatedEntity
Name
Suzanne Thornton
Role
Copyright holder
Affiliation
Rutgers University. School of Graduate Studies
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Author Agreement License
Detail
I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
RightsEvent
Type
Embargo
DateTime (encoding = w3cdtf); (qualifier = exact); (point = start)
2019-10-31
DateTime (encoding = w3cdtf); (qualifier = exact); (point = end)
2020-05-01
Detail
Access to this PDF has been restricted at the author's request. It will be publicly available after May 1st, 2020.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
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2019-06-27T10:51:56
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