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: Statistical Inference for Models with Intractable Normalizing Constants
  name:
    name part: Jin, Ick Hoon
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Liang, Faming
    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: 2013
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource.
  abstract: In this dissertation, we have proposed two new algorithms for statistical inference for models with intractable normalizing constants: the Monte Carlo Metropolis-Hastings algorithm and the Bayesian Stochastic Approximation Monte Carlo algorithm. The MCMH algorithm is a Monte Carlo version of the Metropolis-Hastings algorithm. At each iteration, it replaces the unknown normalizing constant ratio by a Monte Carlo estimate. Although the algorithm violates the detailed balance condition, it still converges, as shown in the paper, to the desired target distribution under mild conditions. The BSAMC algorithm works by simulating from a sequence of approximated distributions using the SAMC algorithm. A strong law of large numbers has been established for BSAMC estimators under mild conditions. One significant advantage of our algorithms over the auxiliary variable MCMC methods is that they avoid the requirement for perfect samples, and thus it can be applied to many models for which perfect sampling is not available or very expensive. In addition, although the normalizing constant approximation is also involved in BSAMC, BSAMC can perform very robustly to initial guesses of parameters due to the powerful ability of SAMC in sample space exploration. BSAMC has also provided a general framework for approximated Bayesian inference for the models for which the likelihood function is intractable: sampling from a sequence of approximated distributions with their average converging to the target distribution. With these two illustrated algorithms, we have demonstrated how the SAMCMC method can be applied to estimate the parameters of ERGMs, which is one of the typical examples of statistical models with intractable normalizing constants. We showed that the resulting estimate is consistent, asymptotically normal and asymptotically efficient. Compared to the MCMLE and SSA methods, a significant advantage of SAMCMC is that it overcomes the model degeneracy problem. The strength of SAM…
  note: by Ick Hoon Jin.
  note: "Major Subject: Statistics"
  note: Includes vita.
  note: Doctor of Philosophy Texas A & M University 2011 http://hdl.handle.net/1969.1/150938
  note: Includes bibliographical references.
  note: Text (Dissertation)
  subject:
    topic: Major Statistics
  subject:
    topic: Autulogistic Model
  subject:
    topic: Ising Model
  subject:
    topic: Stochastic Approximation Monte Carlo
  subject:
    topic: Exponential Random Graph Models
  subject:
    topic: Markov Chain Monte Carlo
  subject:
    topic: Intractable Normalizing Constants
  identifier: http://hdl.handle.net/1969.1/150938
  record info:
    record content source: TXA
    record creation date: 140326
    record change date: 20151206092819.0
    record identifier: in00003453526
    language of cataloging:
      language term: eng