plgp (version 1.0)

draw.GP: Metropolis-Hastings draw for GP parameters

Description

Functions for using Metropolis-Hastings (MH) to evolve a particle according to the posterior distribution given by a Gaussian process (GP) for regression, classification, or combined unknown constraint model

Usage

draw.GP(Zt, prior, l = 3, h = 4, thin = 10, Y = NULL)
draw.CGP(Zt, prior, l = 3, h = 4, thin = 10)
draw.ConstGP(Zt, prior, l = 3, h = 4, thin = 10)

Arguments

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

l

positive uniform random walk parameter; for old parameter pold, a new parameter is proposed as p = runif(1, p*l/h, p*h/l). Such proposals are then accepted (or rejected) via the MH acceptance ratio

h

positive uniform random walk parameter; see above

thin

thinning level in the MCMC; describes the number of MH rounds executed before the value is saved as a sample from the (marginal) posterior distribution

Y

not for external use; used internally by CGP and ConstGP internal routines

Value

• These functions return an updated particle Zt

Details

These functions are used in two important places in plgp. At the user level, they can be used to initialize the particles at time start; see PL and the demos. Internally, they are used in the PL propagate step, e.g., propagate.GP

draw.ConstGP is a combination of the draw.GP and draw.CGP methods, which are for regression and classification GPs, 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

See Also

init.GP, propagate.GP, PL

Examples

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