# s.chi: Variance estimator In emulator: Bayesian Emulation of Computer Programs

## Description

Returns estimator for a priori sigma^2

## Usage

 `1` ```s.chi(H, Ainv, d, s0 = 0, fast.but.opaque = TRUE) ```

## Arguments

 `H` Regression basis function (eg that returned by `regressor.multi()`) `Ainv` inv(A) where A is a correlation matrix (eg that returned by `corr.matrix()`) `d` Vector of data points `s0` Optional offset `fast.but.opaque` Boolean, with default `TRUE` meaning to use `quad.form()`, and `FALSE` meaning to use straightforward `%*%`. The first form should be faster, but the code is less intelligible than the second form. Comparing the returned value with this argument on or off should indicate the likely accuracy attained.

## Details

See O'Hagan's paper (ref below), equation 12 for details and context.

## Author(s)

Robin K. S. Hankin

## References

A. O'Hagan 1992. “Some Bayesian Numerical Analysis”, pp345-363 of Bayesian Statistics 4 (ed J. M. Bernardo et al), Oxford University Press

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22``` ```# example has 10 observations on 6 dimensions. # function is just sum( (1:6)*x) where x=c(x_1, ... , x_2) data(toy) val <- toy colnames(val) <- letters[1:6] H <- regressor.multi(val) d <- apply(H,1,function(x){sum((0:6)*x)}) # create A matrix and its inverse: A <- corr.matrix(val,scales=rep(1,ncol(val))) Ainv <- solve(A) # add some suitably correlated noise: d <- as.vector(rmvnorm(n=1, mean=d, 0.1*A)) # now evaluate s.chi(): s.chi(H, Ainv, d) # assess accuracy: s.chi(H, Ainv, d, fast=TRUE) - s.chi(H, Ainv, d, fast=FALSE) ```

emulator documentation built on Jan. 15, 2019, 9:03 a.m.