The Prior Distribution in Bayesian Statistics

A major problem associated with Bayesian estimation is selecting the prior distribution. The more recent literature on the selection of the prior is reviewed. Very little of a general nature on the selection of the prior is formed in the literature except for non-informative priors. This class of priors is seen to have limited usefulness. A method of selecting an informative prior is generalized in this thesis to include estimation of several parameters using a multivariate prior distribution. The concepts required for quantifying prior information is based on intuitive principles. In this way, it can be understood and controlled by the decision maker (i.e., those responsible for the consequences) rather than analysts. The information required is: (1) prior point estimates of the parameters being estimated and (2) an expression of the desired influence of the prior relative to the present data in determining the parameter estimates (e.g., item (2) implies twice as much influence as the data). These concepts (point estimates and influence) may be used equally with subjective or quantitative prior information