Hypotheses regarding the distribution, texture and trace element concentrations of lake sediments were tested by empirical analyses of multi-lake data sets (52 to 83 lakes). Sediment distribution was best characterized by the deposition boundary depth (DBD), the abrupt transition from coarse- to fine-grained sediments. The DBD can now be predicted from either empirical models or empirical-theoretical simplifications of wave of sediment threshold theory, both in terms of exposure (or fetch) and bottom slope. The texture (organic content, water content and bulk density) of profundal sediments was related to the inorganic sedimentation rate and exposure, but not to the lake trophic status or the net organic matter sedimentation rate. The relationships between sediment texture and intra- and inter-site variability, together with the models that predict the DBD and sediment texture, were used to develop an algorithm that should greatly reduce sampling effort in lake sediment surveys. Finally, sediment trace element concentrations were predicted from sediment texture, site depth and simple geologic classifications. The models developed here, provide a framework in which to sample lake sediments and interpret their properties.

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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.

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