rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Multivariate Normal Probability, Truncated Sampling, and Approximation for Statistical Modeling
  name:
    name part: Ding, Patrick
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Pati, Debdeep
    role:
      role term: thesis advisor.
  name:
    name part: Texas A&M University
    role:
      role term: degree granting institution.
  type of resource: text
  genre: bibliography
  origin info:
    place:
      place term: txu
    date issued: 2023
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource.
  abstract: This dissertation contains four projects involving applications of truncated multivariate normal sampling and multivariate normal probability estimation for linearly constrained domains. These two problems have a large number of applications in various statistical modeling domains. They are also very challenging to solve efficiently and accurately for small probability domains, which inevitably occurs as the dimension of the multivariate normal increases. Thus models that depend on such components demand scalable and accurate samplers and probability estimation methods. The first project is a survey of truncated multivariate normal sampling and multivariate normal probability estimation. We provide exposition on commonly used samplers and probability estimation methods in the literature, and trace their development. We provide C++ implementations of important methods, and compare them on synthetic and realistic examples to gauge their scalability and accuracy. The second project is an application of expectation propagation for multivariate normal approximation to multinomial probit modeling with sparsity constraints on the latent precision. We use the approximation to compute moments of truncated multivariate normals for an expectation maximization algorithm. The third project is an application of expectation propagation to a weighted Gaussian graphical model for heterogenous graph modeling. We explore using the full covariance multivariate normal approximation and inclusive Kullback Leibler divergence objective of expectation propagation and find improved performance compared to a simpler mean field normal variational inference approximation. The final project introduces a measure for quantifying the relative effective sample size between Gaussian processes with different covariance kernels. This provides insight on an important hyperparameter for Gaussian process regression. The electronic version of this dissertation is accessible from https://hdl.handle.net/1969…
  note: by Patrick Ding.
  note: "Major Subject: Statistics"
  note: Includes vita.
  note: Doctor of Philosophy Texas A&M University 2022 https://hdl.handle.net/1969.1/198024
  note: Includes bibliographical references.
  note: Text (Dissertation)
  subject:
    topic: Major Statistics
  subject:
    topic: expectation propagation
  subject:
    topic: Gaussian process
  subject:
    topic: sampling
  subject:
    topic: orthant
  subject:
    topic: spatial
  subject:
    topic: probit
  subject:
    topic: computation
  subject:
    topic: statistics
  subject:
    topic: probability
  subject:
    topic: graphical models
  subject:
    topic: approximation
  subject:
    topic: Monte Carlo
  identifier: https://hdl.handle.net/1969.1/198024
  record info:
    record content source: TXA
    record creation date: 240827
    record change date: 20240829173512.5
    record identifier: in00005468510
    language of cataloging:
      language term: eng