cov.p5.supp: Covariance function for posterior distribution of z In RobinHankin/calibrator: Bayesian Calibration of Complex Computer Codes

Description

Covariance function for posterior distribution of z(.) conditional on estimated hyperparameters and calibration parameters theta.

Usage

 ```1 2``` ```Cov.eqn9.supp(x, xdash=NULL, theta, d, D1, D2, H1, H2, phi) cov.p5.supp (x, xdash=NULL, theta, d, D1, D2, H1, H2, phi) ```

Arguments

 `x` first point, or (`Cov.eqn9.supp()`) a matrix whose rows are the points of interest `xdash` The second point, or (`Cov.eqn9.supp()`) a matrix whose rows are the points of interest. The default of `NULL` means to use `xdash=x` `theta` Parameters. For `Cov.eqn9.supp()`, supply a vector which will be interpreted as a single point in parameter space. For `cov.p5.supp()`, supply a matrix whose rows will be interpreted as points in parameter space `d` Observed values `D1` Code run design matrix `D2` Observation points of real process `H1` Basis function for `D1` `H2` Basis function for `D2` `phi` Hyperparameters

Details

Evaluates the covariance function: the last formula on page 5 of the supplement. The two functions documented here are vectorized differently.

Function `Cov.eqn9.supp()` takes matrices for arguments `x` and `xdash` and a single vector for `theta`. Evaluation is thus taken at a single, fixed value of `theta`. The function returns a matrix whose rows correspond to rows of `x` and whose columns correspond to rows of `xdash`.

Function `cov.p5.supp()` takes a vector for arguments `x` and `xdash` and a matrix for argument `theta` whose rows are the points in parameter space. A vector `V`, with elements corresponding to the rows of argument `theta` is returned:

V[i] = cov(z(x),z(x')|theta[i])

Value

Returns a matrix of covariances

Note

May return the transpose of the desired object

Author(s)

Robin K. S. Hankin

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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18``` ```data(toys) x <- rbind(x.toy,x.toy+1,x.toy,x.toy,x.toy) rownames(x) <- letters[1:5] xdash <- rbind(x*2,x.toy) rownames(xdash) <- LETTERS[1:6] Cov.eqn9.supp(x=x,xdash=xdash,theta=theta.toy,d=d.toy,D1=D1.toy, D2=D2.toy,H1=H1.toy,H2=H2.toy,phi=phi.toy) phi.true <- phi.true.toy(phi=phi.toy) Cov.eqn9.supp(x=x,xdash=xdash,theta=theta.toy,d=d.toy,D1=D1.toy, D2=D2.toy,H1=H1.toy,H2=H2.toy,phi=phi.true) # Now try a sequence of thetas: cov.p5.supp(x=x.toy,theta=t.vec.toy,d=d.toy,D1=D1.toy,D2=D2.toy, H1=H1.toy,H2=H2.toy,phi=phi.toy) ```

RobinHankin/calibrator documentation built on May 8, 2019, 8:06 a.m.