ABSTRACT
This chapter aims to derive conjugate prior distributions for the correlation coefficient between observation vectors. Conjugate prior distributions are informative prior distributions. Conjugate prior distributions follow naturally from classical statistics. It is well known that if a set of data were taken in two parts, then an analysis which takes the first part as a prior for the second part is equivalent to an analysis which takes both parts together. The Conjugate prior distribution for a parameter is of great utility and is obtained by writing down the likelihood, interchanging the roles of the random variable and the parameter, and “enriching” the distribution so that it does not depend on the data set. The Conjugate prior distribution has the property that when combined with the likelihood, the resulting posterior is in the same “family” of distributions. The choice of Conjugate prior distributions have natural updating properties and can simplify the estimation procedure.
