EK.eqn10.supp {calibrator}R Documentation

Posterior mean of K

Description

Estimates the posterior mean of K as per equation 10 of KOH2001S, section 4.2

Usage

EK.eqn10.supp(X.dist, D1, D2, H1, H2, d, hbar.fun,
   lower.theta, upper.theta, extractor, give.info=FALSE,
   include.prior=FALSE, phi, ...)

Arguments

X.dist Probability distribution of X, in the form of a two-element list. The first element is the mean (which should have name “mean”), and the second element is the variance matrix, which should be a positive definite matrix of the correct size, and have name “var”
D1 Matrix whose rows are the code run points
D2 Matrix whose rows are field observation points
H1 Regression function for D1
H2 Regression function for D2
d Vector of code outputs and field observations
include.prior Boolean; passed to function p.eqn8.supp() (qv)
hbar.fun Function that gives expectation (with respect to X) of h1(x,theta) and h2(x) as per section 4.2
lower.theta Lower integration limit for theta (NB: a vector)
upper.theta Lower integration limit for theta (NB: a vector)
extractor Extractor function; see extractor.toy() for an example
give.info Boolean, with default FALSE meaning to return just the answer and TRUE to return the answer along with all output from both integrations as performed by adapt()
phi Hyperparameters
... Extra arguments passed to the integration function. If multidimensional (ie length(theta)>1), then the arguments are passed to adapt(); if one dimensional, they are passed to integrate()

Details

This function evaluates a numerical approximation to equation 10 of section 4.2 of the supplement.

Equation 10 integrates over the prior distribution of theta. If theta is a vector, multidimensional integration is necessary.

In the case of multidimensional integration, the eponymous adapt() is used. Note that, as of version 1.0-3, this is restricted to fewer than 20 dimensions—which is not checked for. Evaluation is slow, as multidimensional integration is hard (spot the understatement).

In the case of one dimensional integration—theta being a scalar—function integrate() of the stats package is used.

Note that equation 10 is conditional on the observed data and the hyperparameters

Value

Returns a scalar

Note

The function was not reviewed by the Journal of Statistical Software

Author(s)

Robin K. S. Hankin

References

Examples

1+1
## Not run: 
# Not run because it takes R CMD check too long.
data(toys)
EK.eqn10.supp(X.dist=X.dist.toy, D1=D1.toy, D2=D2.toy, H1=H1.toy, H2=H2.toy, d=d.toy, hbar.fun=hbar.fun.toy, lower.theta=c(-3,-3,-3), upper.theta=c(3,3,3),extractor=extractor.toy, phi=phi.toy)
## End(Not run)

[Package calibrator version 1.0-58 Index]