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      Cross-validatory Model Comparison and Divergent Regions Detection using iIS and iWAIC for Disease Mapping

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      Date
      2015-04-02
      Author
      Qiu, Shi
      Type
      Thesis
      Degree Level
      Masters
      Metadata
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      Abstract
      The well-documented problems associated with mapping raw rates of disease have resulted in an increased use of Bayesian hierarchical models to produce maps of "smoothed'' estimates of disease rates. Two statistical problems arise in using Bayesian hierarchical models for disease mapping. The first problem is in comparing goodness of fit of various models, which can be used to test different hypotheses. The second problem is in identifying outliers/divergent regions with unusually high or low residual risk of disease, or those whose disease rates are not well fitted. The results of outlier detection may generate further hypotheses as to what additional covariates might be necessary for explaining the disease. Leave-one-out cross-validatory (LOOCV) model assessment has been used for these two problems. However, actual LOOCV is time-consuming. This thesis introduces two methods, namely iIS and iWAIC, for approximating LOOCV, using only Markov chain samples simulated from a posterior distribution based on a full data set. In iIS and iWAIC, we first integrate the latent variables without reference to holdout observation, then apply IS and WAIC approximations to the integrated predictive density and evaluation function. We apply iIS and iWAIC to two real data sets. Our empirical results show that iIS and iWAIC can provide significantly better estimation of LOOCV model assessment than existing methods including DIC, Importance Sampling, WAIC, posterior checking and Ghosting methods.
      Degree
      Master of Science (M.Sc.)
      Department
      Mathematics and Statistics
      Program
      Mathematics
      Supervisor
      Li, Longhai; Feng, Cindy.Xin
      Committee
      Bickis, Mikelis G.
      Copyright Date
      March 2015
      URI
      http://hdl.handle.net/10388/ETD-2015-03-1988
      Subject
      cross-validation
      disease mapping
      importance sampling
      WAIC
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