calibrator (version 1.2-8)

E.theta.toy: Expectation and variance with respect to theta

Description

Function E.theta.toy returns expectation of H_1(D) with respect to \(\theta\); Edash.theta.toy returns expectation with respect to \(E'\). Function E.theta.toy also returns information about nonlinear behaviour of h1(x,theta).

Usage

E.theta.toy(D2=NULL,  H1=NULL, x1=NULL, x2=NULL, phi, give.mean=TRUE)
Edash.theta.toy(x, t.vec, k,  H1, fast.but.opaque=FALSE, a=NULL, b=NULL,
phi=NULL)

Arguments

D2

Observation points

H1

Regression function for D1

phi

hyperparameters. Default value of NULL only to be used in Edash.theta.toy() when fast.but.opaque is TRUE

x

lat/long point (for Edash.theta.toy)

t.vec

Matrix whose rows are parameter values (for Edash.theta.toy)

k

Integer specifying column (for Edash.theta.toy)

give.mean

In E.theta.toy(), Boolean, with default TRUE meaning to return the mean (expectation), and FALSE meaning to return the “variance”

fast.but.opaque

In Edash.theta.toy(), Boolean, with default FALSE meaning to use a slow but clear method. If TRUE, use faster code but parameters a and b must then be specified

a

Constant term, needed if fast.but.opaque is TRUE: \(\left(V_\theta^{-1}+2\Omega_t\right)^{-1}V_\theta^{-1}m_\theta\). Specifying a in advance saves execution time

b

Linear term, needed if fast.but.opaque is TRUE: \(2\left(V_\theta^{-1}+2\Omega_t\right)^{-1}\Omega_t\) (multiplied by t[k,] in Edash.theta.toy()).

x1

In E.theta.toy(g=F,...), the value of x in \(h_1(x,\theta)\). The default value is NULL because in simple cases such as that implemented here, the output is independent of x1 and x2

x2

In E.theta.toy(g=F,...), the value of x in \(h_1(x,\theta)\)

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)

See Also

toys

Examples

# NOT RUN {
data(toys)
E.theta.toy(D2=D2.toy,      H1=H1.toy,phi=phi.toy)
E.theta.toy(D2=D2.toy[1,],  H1=H1.toy,phi=phi.toy)
E.theta.toy(D2=x.toy,       H1=H1.toy,phi=phi.toy)
Edash.theta.toy(x=x.toy,t.vec=t.vec.toy,k=1, H1=H1.toy,phi=phi.toy)
# }