Description Usage Arguments Details Value Author(s) References See Also Examples
Calculates the three integrals needed for V
, under the
restrictions specified in the KOH2001 supplement
1 2 3 4 5 |
D1 |
Matrix of code run points |
H1 |
regression basis functions for |
extractor |
Function to extract |
x |
Lat and long of a point in |
x.i |
Lat and long of first point (eg |
x.j |
Lat and long of second point (eg |
theta |
parameters |
Edash.theta |
Function to return expectation of |
E.theta |
Function to return expectation of |
test.for.symmetry |
In Set this argument to |
fast.but.opaque |
In |
x.star |
In |
t.vec |
In |
method |
In |
phi |
Hyperparameters |
The four functions return integrals representing means taken over
theta
. To wit:
Function tt.fun()
evaluates
int t(x_j,θ)t(x_i,θ)^T p(theta) d(theta)
and is used in
V.fun()
. Note that this function is symmetric in x_i
and x_j.
Function ht.fun()
evaluates
int h_1(x_j,θ)t(x_i,θ)^T p(theta) d(theta)
and is used in
V.fun()
. Note that this function is not symmetric in
x_i and x_j.
Function
hh.fun()
evaluates
int h_1(x_j,θ)h_1(x_i,θ)^T p(theta) d(theta)
and is used in
V.fun()
. Note that this function is symmetric in x_i
and x_j.
Function t.fun()
evaluates
int t(x_i,θ)^T p(theta) d(theta)
using the formula
<omitted; see pdf>
It is used in Ez_eq7.supp()
. NB: do not confuse
this function with tee()
, which is different.
These functions are not generally of much interest to the end user; they
are called by V.fun()
. They are defined separately as a
debugging aid, and to simplify the structure of V.fun()
.
Each function returns a matrix as described in KOH2001
Robin K. S. Hankin
M. C. Kennedy and A. O'Hagan 2001. Bayesian calibration of computer models. Journal of the Royal Statistical Society B, 63(3) pp425-464
M. C. Kennedy and A. O'Hagan 2001. Supplementary details on Bayesian calibration of computer models, Internal report, University of Sheffield. Available at http://www.tonyohagan.co.uk/academic/ps/calsup.ps
R. K. S. Hankin 2005. Introducing BACCO, an R bundle for Bayesian analysis of computer code output, Journal of Statistical Software, 14(16)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | data(toys)
tt.fun(D1=D1.toy, extractor=extractor.toy, x.i=D2.toy[1,],
x.j=D2.toy[2,], phi=phi.toy)
ht.fun(x.i=D2.toy[1,], x.j=D2.toy[2,], D1=D1.toy,
extractor=extractor.toy,
Edash.theta=Edash.theta.toy, H1=H1.toy, fast.but.opaque=FALSE, phi=phi.toy)
ht.fun(x.i=D2.toy[1,], x.j=D2.toy[2,], D1=D1.toy,
extractor=extractor.toy,
Edash.theta=Edash.theta.toy, H1=H1.toy, fast.but.opaque=TRUE,
x.star=extractor.toy(D1.toy)$x.star, t.vec=extractor.toy(D1.toy)$t.vec,
phi=phi.toy)
hh.fun(x.i=D2.toy[1,], x.j=D2.toy[2,],
H1=H1.toy, E.theta=E.theta.toy, phi=phi.toy)
t.fun(x=x.toy, D1=D1.toy, extractor=extractor.toy, phi=phi.toy)
|
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