reality: Reality

Description

Function to compute reality, gratis deus ex machina. Includes a simple computer model that substitutes for a complex climate model, and a simple function that substitutes for the base system, in this case the climate.

Usage

model.inadequacy(X, set.seed.to.zero=TRUE, draw.from.prior=FALSE,
     export.true.hyperparameters=FALSE,phi=NULL)
computer.model(X, params=NULL, set.seed.to.zero=TRUE,
draw.from.prior=FALSE, export.true.hyperparameters=FALSE,phi=NULL)
phi.true.toy(phi)

Arguments

Observation point

params

Parameters needed by computer.model()

set.seed.to.zero

Boolean, with the default value of TRUE meaning to set the RNG seed to zero

draw.from.prior

Boolean, with default FALSE meaning to generate obsevations from the “true” values of the parameters, and TRUE meaning to draw from the relevant apriori distribution.

export.true.hyperparameters

Boolean, with default value of FALSE meaning to return the observed scalar. Set to TRUE to exercise omniscience and access the true values of the parameters and hyperparameters. Only the omnipotent should set this variable, and only the omniscient may see its true value.

phi

In function phi.true.toy() the hyperparameters \(\phi\). Note that apriori distributions are unchanged (they are irrelevant to omniscient beings).

In functions reality() and computer.model(), the prior distributions of the hyperparameters is passed via phi (so it only elements psi1.apriori and psi2.apriori need to be set).

Details

Function reality() provides the scalar value observed at a point x. Evaluation expense is zero; there is no overhead.

(However, it does not compute “reality”: the function returns a value subject to observational error \(N(0,\lambda)\) as per equation 5. It might be better to call this function observation())

Function computer.model() returns the output of a simple, nonlinear computer model.

Both functions documented here return a random variable drawn from an appropriate (correlated) multivariate Gaussian distribution, and are thus Gaussian processes.

The approach is more explicit in the help pages of the emulator package. There, Gaussian processes are generated by directly invoking rmvnorm() with a suitable correlation matrix

References

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)

Examples

Run this code

# NOT RUN {
  data(toys)


  computer.model(X=D2.toy,params=theta.toy)
  computer.model(D1.toy)
  computer.model(X=x.toy, params=extractor.toy(D1.toy)$t.vec)


  phi.fix <- phi.change(old.phi=phi.toy,
           psi1=c(1, 0.5, 1, 1, 0.5,  0.4),phi.fun=phi.fun.toy)
      #The values come from c(REAL.SCALES,REAL.SIGMA1SQUARED) as
      #seen in the sourcecode for computer.model().

  computer.model(D1.toy)   # use debug(computer.model) and examine
                           # var.matrix directly.  It should match the
                           #  output from V1():


          # first fix phi so that it has the correct values for psi1 (see the
          # section on psi1 in ?phi.fun.toy for how to get this):

   phi.fix <- phi.change(old.phi=phi.toy,psi1=c(1, 0.5, 1.0, 1.0, 0.5,
   0.4), phi.fun=phi.fun.toy)
   V1(D1.toy,phi=phi.fix)





# What are the hyperparameters that were used to create reality?
phi.true.toy(phi=phi.toy)

# 
 computer.model(X=D2.toy,params=theta.toy,draw.from.prior=TRUE,phi=phi.toy)


# }