approximator (version 1.2-7)

Pi: Kennedy's Pi notation

Description

Evaluates Kennedy's \(\prod\) product

Usage

Pi(hpa, i, j)

Arguments

hpa

Hyperparameter object

i

subscript

j

superscript

Author

Robin K. S. Hankin

Details

This function evaluates Kennedy's \(\prod\) product, but with the additional feature that \(\prod_i^j=0\) if \(i>j+1\). This seems to work in practice.

References

M. C. Kennedy and A. O'Hagan 2000. “Predicting the output from a complex computer code when fast approximations are available” Biometrika, 87(1): pp1-13

Examples

data(toyapps)
Pi(hpa.toy,1,2)
Pi(hpa.toy,2,2)
Pi(hpa.toy,3,2)
Pi(hpa.toy,4,2)