Exact Bayesian Higher Posterior Density Interval for the Correlation Coefficient of a Normal Bivariate Distribution

This paper proposes a new procedure for computing the extremes of the highest posterior density (H.P.D.) interval of the correlation coefficient of a normal bivariate distribution. The procedure uses the exact expression of the correlation coefficient distribution function, which is based on noninformative priors of the parameters of the normal distribution, and avoids the numerical integration required by the commonly adopted expression. The extremes of the highest posterior density interval are implemented as routines in the symbolic programming language Mathematica.