show.rcalibration: Show an Robust Calibration object.

In RobustCalibration: Robust Calibration of Imperfect Mathematical Models

Show an Robust Calibration object.

Description

Function to print the Robust Calibration model after the rcalibration class has been constructed.

Usage

## S4 method for signature 'rcalibration'
show(object)

Arguments

object

an object of class rcalibration.

Author(s)

Mengyang Gu [aut, cre]

Maintainer: Mengyang Gu <[e-mail]>

References

A. O'Hagan and M. C. Kennedy (2001), Bayesian calibration of computer models, Journal of the Royal Statistical Society: Series B (Statistical Methodology, 63, 425-464.

M. Gu (2016), Robust Uncertainty Quantification and Scalable Computation for Computer Models with Massive Output, Ph.D. thesis., Duke University.

M. Gu and L. Wang (2017) Scaled Gaussian Stochastic Process for Computer Model Calibration and Prediction. arXiv preprint arXiv:1707.08215.

M. Gu (2018) Jointly Robust Prior for Gaussian Stochastic Process in Emulation, Calibration and Variable Selection . arXiv preprint arXiv:1804.09329.

Examples

##-------------------------------------------------
#A simple example where the math model is not biased
##-------------------------------------------------
## the reality 
test_funct_eg1<-function(x){
  sin(pi/2*x)
}



## obtain 15 data from the reality plus a noise
set.seed(1)
## 10 data points are very small, one may want to add more data
n=15
input=seq(0,4,4/(n-1))
input=as.matrix(input)

output=test_funct_eg1(input)+rnorm(length(input),mean=0,sd=0.2)

## plot input and output 
#plot(input,output)
#num_obs=n=length(output)



## the math model 
math_model_eg1<-function(x,theta){
  sin(theta*x)  
}

##fit the S-GaSP model for the discrepancy
##one can choose the discrepancy_type to GaSP, S-GaSP or no discrepancy
##p_theta is the number of parameters to calibrate and user needs to specifiy 
##one may also want to change the number of posterior samples by change S and S_0
##one may change sd_proposal for the standard derivation of the proposal distribution
## one may also add a mean by setting X=... and have_trend=TRUE
model_sgasp=rcalibration(design=input, observations=output, p_theta=1,simul_type=1,
                         math_model=math_model_eg1,theta_range=matrix(c(0,3),1,2)
                         ,S=10000,S_0=2000,discrepancy_type='S-GaSP')


##posterior samples of calibration parameter and value
## the value is 
plot(model_sgasp@post_sample[,1],type='l',xlab='num',ylab=expression(theta))   
plot(model_sgasp@post_value,type='l',xlab='num',ylab='posterior value')   


show(model_sgasp)


#-------------------------------------------------------------
# an example with multiple local maximum of minimum in L2 loss
#-------------------------------------------------------------

## the reality 
test_funct_eg1<-function(x){
  x*cos(3/2*x)+x
}



## obtain 15 data from the reality plus a noise
set.seed(1)
n=15
input=seq(0,5,5/(n-1))
input=as.matrix(input)

output=test_funct_eg1(input)+rnorm(length(input),mean=0,sd=0.05)

num_obs=n=length(output)


## the math model 
math_model_eg1<-function(x,theta){
  sin(theta*x)+x  
}

## fit the S-GaSP model for the discrepancy

model_sgasp=rcalibration(design=input, observations=output, p_theta=1,simul_type=1,
                         math_model=math_model_eg1,theta_range=matrix(c(0,3),1,2),
                         discrepancy_type='S-GaSP')


## posterior samples 
plot(model_sgasp@post_sample[,1],type='l',xlab='num',ylab=expression(theta))   
show(model_sgasp)

RobustCalibration documentation built on June 22, 2024, 10:37 a.m.