lpredprob.GP: Log-Predictive Probability Calculation for GPs

Description

Log-predictive probability calculation for Gaussian process (GP) regression, classification, or combined unknown constraint models; primarily to be used particle learning (PL) re-sample step

Usage

lpredprob.GP(z, Zt, prior)
lpredprob.CGP(z, Zt, prior)
lpredprob.ConstGP(z, Zt, prior)

Arguments

new observation whose (log) predictive probability is to be calculated given the particle Zt

the particle describing model parameters and sufficient statistics that determines the predictive distribution

prior

prior parameters passed from PL generated by one of the prior functions, e.g., prior.GP

Value

Returns a real-valued scalar - the log predictive probability

Details

This is the workhorse of the PL re-sample step. For each new observation (in sequence), the PL function calls lpredprob and these values determine the weights used in the sample function to obtain the new particle set, which is then propagated, e.g., using propagate.GP

The lpredprob.ConstGP is essentially the combination (product) of lpredprob.GP and lpredprob.CGP for regression and classification GP models, respectively

References

Gramacy, R. and Polson, N. (2010). Particle learning of Gaussian process models for sequential design and optimization. Tech. Rep. arXiv:0909.5262, University of Cambridge.

Gramacy, R. and Lee, H. (2010). Optimization under unknown constraints. Bayesian Statistics 9, J. M. Bernardo, M. J. Bayarri, J. O. Berger, A. P. Dawid, D. Heckerman, A. F. M. Smith and M. West (Eds.); Oxford University Press

http://www.statslab.cam.ac.uk/~bobby/plgp.html

Examples

Run this code

## See the demos via demo(package="plgp") and the examples
## section of ?plgp

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