BACCO (version 1.0-50)

phi.fun.toy: Functions to create or change hyperparameters

Description

Function to create (phi.fun.toy) or modify (phi.change) toy hyperparameters $\phi$ in a form suitable for passing to the other functions in the library.

The user should never make $\phi$ by hand; always use one of these functions.

Usage

phi.fun.toy(rho, lambda, psi1, psi1.apriori, psi2, psi2.apriori,
  theta.apriori, power)
phi.change(phi.fun, old.phi = NULL, rho = NULL, lambda = NULL,
          psi1 = NULL, psi1.apriori=NULL,  psi1.apriori.mean=NULL,  psi1.apriori.sigma=NULL,
          psi2 = NULL, psi2.apriori=NULL,  psi2.apriori.mean=NULL,  psi2.apriori.sigma=NULL,
                      theta.apriori=NULL, theta.apriori.mean=NULL, theta.apriori.sigma=NULL,
          power=NULL)

Arguments

phi.fun

In phi.change(), the name of the function that creates the hyperparameters. Use phi.fun.toy() for the toy dataset

old.phi

In function phi.change(), the hyperparameter object $\phi$ to be modified

rho

Correlation hyperparameter appearing in main equation

lambda

Noise hyperparameter

psi1

Roughness lengths hyperparameter for design matrix D1. Internal function pdm.maker.psi1() takes psi1 as an argument and returns omega_x, omega_t and sigma1squared.

psi1.apriori

A priori PDF for $\psi_1$. In the form

of a two element list with first element (mean) the mean and second element (sigma) the covariance matrix; distribution of the logarithms is assumed to be multivariate normal.

psi1.apriori.mean

In function phi.change.toy(), use this argument to change just the mean of psi1 (and leave the value of sigma unchanged)

psi1.apriori.sigma

In function phi.change.toy(), use this argument to change just the variance matrix of psi1

psi2

Roughness lengths hyperparameter for D2.

Internal function pdm.maker.psi2() takes psi2 as an argument and returns omegastar_x and sigma2squared. In phi.fun.toy(), t

psi2.apriori

A priori PDF for $\psi_2$ and hyperparameters $\rho$ and $\lambda$ (in that order). As for psi1.apriori, this is in the form of a list with the first element (mean) the mean and second eleme

psi2.apriori.mean

In phi.change.toy(), use to change just the mean of psi2

psi2.apriori.sigma

In phi.change.toy(), use to change just the variance matrix of psi2

theta.apriori

Apriori PDF for $\theta$. As above, in the form of a list with elements for the mean and covariance. The distribution is multivariate normal (NB: The distribution is multivariate normal and NOT lognormal! To be explicit: $\log(\theta)$

theta.apriori.mean

In phi.change.toy(), use to change just the mean of theta

theta.apriori.sigma

In phi.change.toy(), use to change just the variance matrix of theta

power

Exponent of the exponential as passed to corr.matrix() (and thence to corr()) of package emulator. For the general case of nondiagonal positive.definite.matrix, the metric is $e^{-\left| (x

Value

• Returns a list of several elements:
• rho
  Correlation hyperparameter
• lambda
  Noise hyperparameter
• psi1
  Roughness lengths hyperparameter for D1
• psi1.apriori
  Apriori mean and variance matrix for psi1
• psi2
  Roughness lengths hyperparameter for D2
• psi2.apriori
  Apriori mean and variance matrix for psi2
• theta.apriori
  Apriori mean and variance matrix for the parameters
• power
  Power for use in the correlation matrix
• omega_x
  Positive definite matrix for the lat/long part of D1, whose diagonal is psi1[1:2]
• omega_t
  Positive definite matrix for the code parameters theta, whose diagonal is psi1[3:5]
• omegastar_x
  Positive definite matrix for use in equation 13 of the supplement; represents distances between rows of D2
• sigma1squared
  variance
• sigma2squared
  variance
• omega_x.upper
  Upper triangular Cholesky decomposition for omega_x
• omega_x.lower
  Lower triangular Cholesky decomposition for omega_x
• omega_t.upper
  Upper triangular Cholesky decomposition for omega_t
• omega_t.lower
  Lower triangular Cholesky decomposition for omega_t
• a
  Precalculated matrix for use in Edash.theta(...,fast.but.opaque=TRUE)
• b
  Precalculated matrix for use in Edash.theta(...,fast.but.opaque=TRUE)
• c
  Precalculated scalar for use in ht.fun(...,fast.but.opaque=TRUE)
• A
  Precalculated scalarfor use in tt.fun()
• A.upper
  Upper triangular Cholesky decomposition for A
• A.lower
  Lower triangular Cholesky decomposition for A

Details

Note that this toy function contains within itself pdm.maker.toy() which extracts omega_x and omega_t and sigma1squared from psi1. This will need to be changed for real-world applications. Earlier versions of the package had pdm.maker.toy() defined separately.

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.shef.ac.uk/~st1ao/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)

See Also

toys, H1.toy

Examples

phi.fun.toy(100,101,1:6,list(mean=rep(1,6),sigma=1+diag(6)),50:55,
list(mean=rep(0,4),sigma=0.1+diag(4)),
list(mean=0.1+(1:3),sigma=2.1+diag(3)),
2)

phi.fun.toy(rho=1,
lambda=1,
psi1          = structure(c(1.1, 1.2, 1.3, 1.4,1.5,0.7), .Names = c("x", "y", "A","B", "C","s1sq")),
psi1.apriori  = list(mean=rep(0,6),sigma=0.4+diag(6)),psi2=structure(c(2.1, 2.2), .Names = c("x","y")),
psi2.apriori  = list(mean=rep(0,5),sigma=0.2+diag(5)),
theta.apriori = list(mean=0.1+(1:3),sigma=2.1+diag(3)),
power=2)

data(toys)
phi.change(phi.fun=phi.fun.toy, old.phi = phi.toy, rho = 100)
phi.change(phi.fun=phi.fun.toy, old.phi = phi.toy, theta.apriori.sigma = 4*diag(3))

identical(phi.toy, phi.change(phi.fun=phi.fun.toy, old.phi=phi.toy))