Statistical methods for the analysis of covariance and spatio-temporal models

A new hierarchical model is proposed for the analysis of covariance with random, unequal variances. Bayesian inference for the new model depends upon uncertainty in the degrees of freedom for a chi-squared distribution. The convergence of MCMC is validated by extremely accurate Laplacian approximations. Practical applications include neuropsychological tests in offender profiling and nutrition data. As a special case, the parallel line model with equal variances is considered, and alternatives to the F-test for the equality of the group effects, including Bayes factors, are investigated. In the final chapter, a self-similarity spatio-temporal model for the pressures of oil wells in an Alaskan oil field is considered, and our Bayesian techniques are extended to this situation with a view towards future interdisciplinary research.

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