Implementation of the Bayesian paradigm for highly parameterised linear models
This thesis re-examines the Bayes hierarchical linear model and the associated issue of variance component estimation in the light of new numerical procedures, and demonstrates that the Bayes linear model is indeed a practical proposition. Technical issues considered include the development of analytical procedures essential for efficient evaluation of the likelihood function, and a partial characterisation of the difficulty of likelihood evaluation. A general non-informative prior distribution for the hierarchical linear model is developed. Extensions to spherically symmetric error distributions are shown to be practicable and useful. The numerical technique enables the sensitivity of the results to the prior structure, error structure and model structure to be investigated. An extended example is considered which illustrates these analytical and numerical techniques in a 15 dimensional problem. A second example provides a critical examination of a British Standards Institute paper, and develops further techniques for handling alternative spherically symmetric error distributions. Recent work on variance component estimation is viewed from the Bayesian perspective, and areas for further work are identified.