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Exact Markov Chain Monte Carlo with Likelihood Approximations for Functional Linear Models

Smith, Corey James

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2018, Doctor of Philosophy, Ohio State University, Statistics.
Functional data analysis is a branch of statistics that deals with the theory and analysis of data which may be comprised of functions in addition to scalar values. Here we consider the linear model that relates functional covariates to scalar responses. We introduce an exact MCMC algorithm which does not rely on likelihood evaluations to estimate the parameter function. The proposed method uses Barker's algorithm (as opposed to Metropolis-Hastings). Though Barker's has been shown to be asymptotically less efficient than Metropolis-Hastings, the form of its acceptance probability allows us to make the accept/reject decision efficiently without needing to evaluate the likelihood function. We utilize unbiased estimates of the log-likelihood function along with two nested Bernoulli factories to accomplish this. In addition, exact MCMC methods for logistic and Poisson regression settings with functional predictors are provided. These latter two models again feature Bernoulli factories and Barker's algorithm while also making use of debiasing techniques to aid in log-likelihood estimation.
Radu Herbei, PhD (Advisor)
Laura Kubatko, PhD (Committee Member)
Matt Pratola, PhD (Committee Member)
Lisa Jordan, PhD (Committee Member)
219 p.

Recommended Citations

Citations

  • Smith, C. J. (2018). Exact Markov Chain Monte Carlo with Likelihood Approximations for Functional Linear Models [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1531833318013379

    APA Style (7th edition)

  • Smith, Corey. Exact Markov Chain Monte Carlo with Likelihood Approximations for Functional Linear Models. 2018. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1531833318013379.

    MLA Style (8th edition)

  • Smith, Corey. "Exact Markov Chain Monte Carlo with Likelihood Approximations for Functional Linear Models." Doctoral dissertation, Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1531833318013379

    Chicago Manual of Style (17th edition)