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      • HARVEST
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      Bayesian analysis for time series of count data

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      OBEIDAT-DISSERTATION.pdf (1.370Mb)
      Date
      2014-07-17
      Author
      Obeidat, Mohammed
      Type
      Thesis
      Degree Level
      Doctoral
      Metadata
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      Abstract
      Time series involving count data are present in a wide variety of applications. In many applications, the observed counts are usually small and dependent. Failure to take these facts into account can lead to misleading inferences and may detect false relationships. To tackle such issues, a Poisson parameter-driven model is assumed for the time series at hand. This model can account for the time dependence between observations through introducing an autoregressive latent process. In this thesis, we consider Bayesian approaches for estimating the Poisson parameter-driven model. The main challenge is that the likelihood function for the observed counts involves a high dimensional integral after integrating out the latent variables. The main contributions of this thesis are threefold. First, I develop a new single-move (SM) Markov chain Monte Carlo (MCMC) method to sample the latent variables one by one. Second, I adopt the idea of the particle Gibbs sampler (PGS) method \citep{andrieu} into our model setting and compare its performance with the SM method. Third, I consider Bayesian composite likelihood methods and compare three different adjustment methods with the unadjusted method and the SM method. The comparisons provide a practical guide to what method to use. We conduct simulation studies to compare the latter two methods with the SM method. We conclude that the SM method outperforms the PGS method for small sample size, while they perform almost the same for large sample size. However, the SM method is much faster than the PGS method. The adjusted Bayesian composite methods provide closer results to the SM than the unadjusted one. The PGS and the selected adjustment method from simulation studies are compared with the SM method via a real data example. Similar results are obtained: first, the PGS method provides results very close to those of the SM method. Second, the adjusted composite likelihood methods provide closer results to the SM than the unadjusted one.
      Degree
      Doctor of Philosophy (Ph.D.)
      Department
      Mathematics and Statistics
      Program
      Mathematics
      Supervisor
      Liu, Juxin
      Committee
      Soteros, Chrisine; Bickis, Mik; Li, Longhai; Osgood, Nathaniel; Gao, Xin
      Copyright Date
      July 2014
      URI
      http://hdl.handle.net/10388/ETD-2014-07-1589
      Subject
      Time series
      count data
      Poisson parameter-driven model
      composite likelihood
      particle Gibbs sampler
      car crashes
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