• Author / Creator
    Nadeem, Khurram
  • Hierarchical models constitute one of the most useful classes of statistical models with applications in a broad range of disciplines including, among others, social sciences, epidemiology and environmental sciences. The widely used linear mixed effects models, their extension to generalized linear mixed models (GLMMs), and state-space models all arise as special cases of general hierarchical models. These models provide a powerful framework for modeling the effects of latent processes, called random effects, whose variability is only manifested through the observed data. However, maximum likelihood estimation for these models poses significant challenges because the likelihood function involves intractable integrals whose dimension depends on the random effects structure. In this thesis, we use data cloning; a simple computational method that exploits advances in Bayesian computation, in particular the Markov Chain Monte Carlo (MCMC) method, to obtain maximum likelihood estimators of the parameters along with their asymptotic standard errors in general hierarchical models. We also suggest a frequentist method to obtain prediction intervals for random effects. Determining estimability of the parameters in a hierarchical model is a very difficult problem in general. This thesis also develops a simple data cloning based graphical test to not only check if the full set of parameters is estimable but also, and more importantly, if a specified function of the parameters is estimable. We exemplify our methodology by analyzing various GLMMs and state-space models. Using a focal population time series of song sparrow (Melospiza melodia) on Mandarte Island, British Columbia, Canada, we show that data cloning can be efficiently employed to fit nonlinear non-Gaussian state-space models for conducting population viability analyses in the presence of observation error and missing values. The quality of MCMC based Bayesian inference, and for that matter, that of data cloning based estimates, is crucially dependent on appropriate diagnosis of MCMC chains’ convergence. This thesis also develops a diagnostic method for convergence of MCMC algorithms using a new empirical characteristic function (ECF) based nonparametric test for comparing k-multivariate distributions. We show that the ECF based convergence diagnostic is particularly useful in cases where the target distribution is multimodal.

  • Subjects / Keywords
  • Graduation date
  • Type of Item
  • Degree
    Doctor of Philosophy
  • DOI
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
  • Institution
    University of Alberta
  • Degree level
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • Statistics
  • Supervisor / co-supervisor and their department(s)
    • Lele, Subhash (Mathematical and Statistical Sciences)
  • Examining committee members and their departments
    • Lele, Subhash (Mathematical and Statistical Sciences)
    • Bruce Smith (Mathematics and Statistics, Dalhousie University)
    • Prasad, Narasimha (Mathematical and Statistical Sciences)
    • Schmuland, Byron (Mathematical and Statistical Sciences)
    • Lewis, Mark (Biological Sciences)