tt.fun {calibrator} | R Documentation |
Calculates the three integrals needed for V
, under the
restrictions specified in the KOH2001 supplement
tt.fun(D1, extractor, x.i, x.j, test.for.symmetry=FALSE, method=1, phi) ht.fun(x.i, x.j, D1, extractor, Edash.theta, H1, fast.but.opaque=TRUE, x.star=NULL, t.vec=NULL, phi) hh.fun(x.i, x.j, H1, E.theta, phi) t.fun(x, D1, extractor, phi)
D1 |
Matrix of code run points |
H1 |
regression basis functions for D1 |
extractor |
Function to extract x.star and t.vec
from D1 |
x |
Lat and long of a point in t.fun() (eg D2[1,] ) |
x.i |
Lat and long of first point (eg D2[1,] ) |
x.j |
Lat and long of second point (eg D2[2,] ) |
theta |
parameters |
Edash.theta |
Function to return expectation of H with respect
to the alternative distribution of theta;
Edash.theta.toy is the example for the toy dataset |
E.theta |
Function to return expectation of H with respect
to theta |
test.for.symmetry |
In tt.fun() , Boolean with TRUE
meaning to calculate each element of C explicitly. If
FALSE , then calculate only the elements of C that
lie on or over the diagonal and use the fact that C is
symmetric to calculate the other matrix elements. For n
observations, this means n(n+1)/2 evaluations,
compared with n^2 for the full case.
Set this argument to TRUE only when debugging, or testing
accuracy. |
fast.but.opaque |
In ht.fun() , Boolean with default
TRUE meaning to pass some precalculated results as
arguments, to save time. Set this argument to FALSE only
when debugging. |
x.star |
In ht.fun() , value of xstar (required
only if fast.but.opaque is TRUE ) |
t.vec |
In ht.fun() , value of t (required
only if fast.but.opaque is TRUE ) |
method |
In tt.fun() , zero means use the old method and
nonzero means use the new method. The new method is faster, but
the code is harder to understand. The two methods should give
identical results. |
phi |
Hyperparameters |
The four functions return integrals representing means taken over
theta
. To wit:
tt.fun()
evaluates int t(x_j,theta)t(x_i,theta)^T p(theta) d(theta)
and is used in
V.fun()
. Note that this function is symmetric in x_i
and x_j.
ht.fun()
evaluates int h_1(x_j,theta)t(x_i,theta)^T p(theta) d(theta)
and is used in
V.fun()
. Note that this function is {bf not} symmetric in x_i
and x_j.
hh.fun()
evaluates int h_1(x_j,theta)h_1(x_i,theta)^T p(theta) d(theta)
and is used in
V.fun()
. Note that this function is symmetric in x_i
and x_j.
t.fun()
evaluates
int t(x_i,theta)^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
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)