c.fun: Correlations between points in parameter space

In approximator: Bayesian Prediction of Complex Computer Codes

Correlations between points in parameter space

Description

Correlation matrices between (sets of) points in parameter space, both prior (c_fun()) and posterior (cdash.fun()).

Usage

c_fun(x, xdash=x, subsets, hpa)
cdash.fun(x, xdash=x, V=NULL, Vinv=NULL, D1, subsets, basis, hpa, method=2)

Arguments

x,xdash	Points in parameter space; or, if a matrix, interpret the rows as points in parameter space. Note that the default value of xdash (viz x) will return the variance-covariance matrix of a set of points
D1	Design matrix
subsets	Subset object
hpa	hyperparameter object
basis	Basis function
V,Vinv	In function cdash.fun(), the data covariance matrix and its inverse. If NULL, the matrix will be calculated from scratch. Supplying a precalculated value for V, and especially Vinv, makes for very much faster execution (edepending on method)
method	Integer specifying which of several algebraically identical methods to use. See the source code for details, but default option 2 seems to be the best. Bear in mind that option 3 does not require inversion of a matrix, but is not faster in practice

Value

Returns a matrix of covariances

Note

Do not confuse function c_fun(), which computes c(x,x') defined just below equation 7 on page 4 with c_t(x,x') defined in equation 3 on page 3.

Consider the example given for two levels on page 4 just after equation 7: c(x,x')=c_2(x,x')+\rho_1^2c_1(x,x') is a kind of prior covariance matrix. Matrix c'(x,x') is a posterior covariance matrix, conditional on the code observations.

Function Afun() evaluates c_t(x,x') in a nice vectorized way.

Equation 7 of KOH2000 contains a typo.

Author(s)

Robin K. S. Hankin

References

KOH2000

See Also

Afun

Examples

data(toyapps)

x <- latin.hypercube(4,3)
rownames(x) <- c("ash" , "elm" , "oak", "pine")
xdash <- latin.hypercube(7,3)
rownames(xdash) <- c("cod","bream","skate","sole","eel","crab","squid")

cdash.fun(x=x,xdash=xdash, D1=D1.toy, basis=basis.toy,subsets=subsets.toy, hpa=hpa.toy)

# Now add a point whose top-level value is known:
x <- rbind(x,D1.toy[subsets.toy[[4]][1],])

cdash.fun(x=x,xdash=xdash, D1=D1.toy, basis=basis.toy,subsets=subsets.toy, hpa=hpa.toy)
# Observe how the bottom row is zero (up to rounding error)

approximator documentation built on Aug. 25, 2023, 1:07 a.m.