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

The implementation of Bayesian predictive procedures under standard normal models is considered. Two distributions are of particular interest, the K-prime and Ksquare 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 recurrence to work properly, a simple solution is proposed which results in a procedure which is intermediate between two classes of algorithms. Some examples of applications are given. Key words: Predictive distribution, Bayesian approach, Incomplete beta function

• Type: Journal
• Year: 2010
• Where: CSDA
• Authors: Jacques Poitevineau, Bruno Lecoutre
• Keywords: Bayesian Predictive Procedures, Beta Function Ratios, CSDA 2010, Incomplete Beta Function