calibrate.bassBasis: Calibrate a bassPCA or bassBasis Model to Data
In BASS: Bayesian Adaptive Spline Surfaces

calibrate.bassBasis

R Documentation

Calibrate a bassPCA or bassBasis Model to Data

Description

Robust modular calibration of a bassPCA or bassBasis emulator using adaptive Metropolis, tempering, and decorrelation steps in an effort to be free of any user-required tuning.

Usage

calibrate.bassBasis(
  y,
  mod,
  type,
  sd.est,
  s2.df,
  s2.ind,
  meas.error.cor,
  bounds,
  discrep.mean,
  discrep.mat,
  nmcmc = 10000,
  temperature.ladder = 1.05^(0:30),
  decor.step.every = 100,
  verbose = T
)

Arguments

`y`	vector of calibration data
`mod`	a emulator of class bassBasis, whose predictions should match y (i.e., predictions from mod should be the same length as y)
`type`	one of c(1,2). 1 indicates a model that uses independent truncation error variance, no measurement error correlation, and discrepancy on a basis while type 2 indicates a model that uses a full truncation error covariance matrix, a full measurement error correlation matrix, a fixed full discrepancy covariance matrix, and a fixed discrepancy mean. 1 is for situations where computational efficiency is important (because y is dense), while 2 is only for cases where y is a short vector.
`sd.est`	vector of prior estimates of measurement error standard deviation
`s2.df`	vector of degrees of freedom for measurement error sd prior estimates
`s2.ind`	index vector, same length as y, indicating which sd.est goes with which y
`meas.error.cor`	a fixed correlation matrix for the measurement errors
`bounds`	a 2xp matrix of bounds for each input parameter, where p is the number of input parameters.
`discrep.mean`	discrepancy mean (fixed), only used if type=2
`discrep.mat`	discrepancy covariance (fixed, for type 2) or basis (if not square, for type 1)
`nmcmc`	number of MCMC iterations.
`temperature.ladder`	an increasing vector, all greater than 1, for tempering. Geometric spacing is recommended, so that you have (1+delta)^(0:ntemps), where delta is small (typically between 0.05 and 0.2) and ntemps is the number of elements in the vector.
`decor.step.every`	integer number of MCMC iterations between decorrelation steps.
`verbose`	logical, whether to print progress.

Details

Fits a modular Bayesian calibration model, with

y = Kw(\theta) + Dv + \epsilon, ~~\epsilon \sim N(0,\sigma^2 R)

f(x) = a_0 + \sum_{m=1}^M a_m B_m(x)

and B_m(x) is a BASS basis function (tensor product of spline basis functions). We use priors

a \sim N(0,\sigma^2/\tau (B'B)^{-1})

M \sim Poisson(\lambda)

as well as the priors mentioned in the arguments above.

Value

An object

Examples

## Not run: 
  ## simulate data (Friedman function)
f<-function(x){
  10*sin(pi*x[,1]*x[,2])+20*(x[,3]-.5)^2+10*x[,4]+5*x[,5]
}
## simulate data (Friedman function with first variable as functional)
sigma<-.1 # noise sd
n<-500 # number of observations
nfunc<-50 # size of functional variable grid
xfunc<-seq(0,1,length.out=nfunc) # functional grid
x<-matrix(runif(n*9),n,9) # 9 non-functional variables, only first 4 matter
X<-cbind(rep(xfunc,each=n),kronecker(rep(1,nfunc),x)) # to get y
y<-matrix(f(X),nrow=n)+rnorm(n*nfunc,0,sigma)

## fit BASS
library(parallel)
mod<-bassPCA(x,y,n.pc=5,n.cores=min(5,parallel::detectCores()))
plot(mod$mod.list[[1]])
plot(mod$mod.list[[2]])
plot(mod$mod.list[[3]])
plot(mod$mod.list[[4]])
plot(mod$mod.list[[5]])

hist(mod$dat$trunc.error)

## prediction
npred<-100
xpred<-matrix(runif(npred*9),npred,9)
Xpred<-cbind(rep(xfunc,each=npred),kronecker(rep(1,nfunc),xpred))
ypred<-matrix(f(Xpred),nrow=npred)
pred<-predict(mod,xpred,mcmc.use=1:1000) # posterior predictive samples (each is a curve)
matplot(ypred,apply(pred,2:3,mean),type='l',xlab='observed',ylab='mean prediction')
abline(a=0,b=1,col=2)
matplot(t(ypred),type='l') # actual
matplot(t(apply(pred,2:3,mean)),type='l') # mean prediction

## sensitivity
sens<-sobolBasis(mod,int.order = 2,ncores = max(parallel::detectCores()-2,1),
                 mcmc.use=1000) # for speed, only use a few samples
plot(sens)


## calibration
x.true<-runif(9,0,1) # what we are trying to learn
yobs<-f(cbind(xfunc,kronecker(rep(1,nfunc),t(x.true)))) +
  rnorm(nfunc,0,.1) # calibration data (with measurement error)
plot(yobs)

cal<-calibrate.bassBasis(y=yobs,mod=mod,
                         discrep.mean=rep(0,nfunc),
                         discrep.mat=diag(nfunc)[,1:2]*.0000001,
                         sd.est=.1,
                         s2.df=50,
                         s2.ind=rep(1,nfunc),
                         meas.error.cor=diag(nfunc),
                         bounds=rbind(rep(0,9),rep(1,9)),
                         nmcmc=10000,
                         temperature.ladder=1.05^(0:30),type=1)

nburn<-5000
uu<-seq(nburn,10000,5)

pairs(rbind(cal$theta[uu,1,],x.true),col=c(rep(1,length(uu)),2),ylim=c(0,1),xlim=c(0,1))

pred<-apply(predict(mod,cal$theta[uu,1,],nugget = T,trunc.error = T,
      mcmc.use = cal$ii[uu]),3,function(x) diag(x)+rnorm(length(uu),0,sqrt(cal$s2[uu,1,1])))
qq<-apply(pred,2,quantile,probs=c(.025,.975))
matplot(t(qq),col='lightgrey',type='l')
lines(yobs,lwd=3)



## End(Not run)
## minimal example for CRAN testing
mod<-bassPCA(1:10,matrix(1:20,10),n.pc=2,nmcmc=2,nburn=1)

BASS documentation built on July 9, 2023, 6:57 p.m.