Implementing Bayesian predictive procedures: The K-prime and K-square distributions

TL;DR

This paper discusses the implementation of Bayesian predictive procedures using K-prime and K-square distributions, providing algorithms and applications for inference on correlation coefficients under normal models.

Contribution

It introduces efficient algorithms for computing the distributions' cumulative functions and addresses numerical issues in recursive calculations.

Findings

Algorithms enable accurate Bayesian inference for correlation coefficients.

Solutions to underflow issues improve computational stability.

Applications demonstrate practical use in statistical inference.

Abstract

The implementation of Bayesian predictive procedures under standard normal models is considered. Two distributions are of particular interest, the K-prime and K-square distributions. They also give exact inferences for simple and multiple correlation coefficients. Their cumulative distribution functions can be expressed in terms of infinite series of multiples of incomplete beta function ratios, thus adequate for recursive calculations. Efficient algorithms are provided. To deal with special cases where possible underflows may prevent a recurrence to work properly, a simple solution is proposed which results in a procedure which is intermediate between two classes of algorithm. Some examples of applications are given.