Description Usage Arguments Value Author(s) References See Also Examples
This function performs the sequential design procedure for
the inverse problem. It starts from an initial design set xi
and selects the followup design points from the candidate set
candei
as per the expected improvement (EI) criterion which is
numerically approximated by the saddlepoint approximation technique in
Huang and Oosterlee (2011). The surrogate is refitted using the
augmented data via svdGP
. After the selection of nadd
followup points, the solution of the inverse problem is estimated
either by the ESL2D
approach or by the SL2D
approach. Details are provided in Chapter 4 of Zhang (2018).
1 2 3 4 5 
xi 
An 
yi 
An L by 
yobs 
A vector of length L of the timeseries valued field observations or the target response. 
nadd 
The number of the followup design points selected by this function. 
candei 
An 
candest 
An 
func 
An R function of the dynamic computer simulator. The
first argument of 
... 
The remaining arguments of the simulator 
mtype 
The type of mean functions for the GP models. The choice "zmean" denotes zeromean, "cmean" indicates constantmean, "lmean" indicates linearmean. The default choice is "zmean". 
estsol 
The method for estimating the final solution to the inverse problem after all followup design points are included, "ESL2D" denotes the ESL2D approach, "SL2D" denotes the SL2D approach. The default choice is "ESL2D". 
frac 
The threshold in the cumulative percentage criterion to select the number of SVD bases. The default value is 0.95. 
nstarts 
The number of starting points used in the numerical maximization of
the posterior density function. The larger 
gstart 
The starting number and upper bound for estimating the
nugget parameter. If 
nthread 
The number of threads (processes) used in parallel execution of this
function. 
clutype 
The type of cluster in the R package "parallel" to perform
parallelization. The default value is "PSOCK". Required only if

xx 
The design set selected by the sequential design approach, which includes both the initial and the followup design points. 
yy 
The response matrix collected on the design set 
xhat 
The estimated solution to the inverse problem obtained on the
candidate set 
maxei 
A vector of length 
Ru Zhang heavenmarshal@gmail.com,
C. Devon Lin devon.lin@queensu.ca,
Pritam Ranjan pritamr@iimidr.ac.in
Huang, X. and Oosterlee, C. W. (2011) Saddlepoint approximations for expectations and an application to CDO pricing, SIAM Journal on Financial Mathematics, 2(1) 692714.
Zhang, R. (2018) Modeling and Analysis of Dynamic Computer Experiments, PhD thesis, Queen's University, ON, Canada.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27  library("lhs")
forretal < function(x,t,shift=1)
{
par1 < x[1]*6+4
par2 < x[2]*16+4
par3 < x[3]*6+1
t < t+shift
y < (par1*t2)^2*sin(par2*tpar3)
}
timepoints < seq(0,1,len=200)
xi < lhs::randomLHS(30,3)
candei < lhs::randomLHS(500,3)
candest < lhs::randomLHS(500,3)
candest < rbind(candest, xi)
## evaluate the response matrix on the design matrix
yi < apply(xi,1,forretal,timepoints)
x0 < runif(3)
y0 < forretal(x0,timepoints)
yobs < y0+rnorm(200,0,sd(y0)/sqrt(50))
ret < saEI(xi,yi,yobs,1,candei,candest,forretal,timepoints,
nstarts=1, nthread=1)
yhat < forretal(ret$xhat,timepoints)
## draw a figure to illustrate
plot(y0,ylim=c(min(y0,yhat),max(y0,yhat)))
lines(yhat,col="red")

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