EK.eqn10.supp {calibrator} | R Documentation |
Estimates the posterior mean of K as per equation 10 of KOH2001S, section 4.2
EK.eqn10.supp(X.dist, D1, D2, H1, H2, d, hbar.fun, lower.theta, upper.theta, extractor, give.info=FALSE, include.prior=FALSE, phi, ...)
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() |
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
Returns a scalar
The function was not reviewed by the Journal of Statistical Software
Robin K. S. Hankin
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)