To cite the `emulator`

package in publications please use Hankin 2005. The `emulator`

package provides R-centric functionality for working with Gaussian processes. The focus is on approximate evaluation of complex computer codes. The package is part of the the `BACCO`

suite of software.

You can install the released version of permutations from CRAN with:

```
# install.packages("emulator") # uncomment this to use the package
library("emulator")
#> Loading required package: mvtnorm
```

The package is maintained on github.

`emulator`

package in useSuppose we have a complicated computer program which takes three parameters as input, and we can run it a total of seven times at different points in parameter space:

```
val
#> alpha beta gamma
#> [1,] 0.7857 0.9286 0.6429
#> [2,] 0.0714 0.3571 0.2143
#> [3,] 0.5000 0.2143 0.7857
#> [4,] 0.3571 0.7857 0.3571
#> [5,] 0.9286 0.5000 0.0714
#> [6,] 0.2143 0.0714 0.5000
#> [7,] 0.6429 0.6429 0.9286
d
#> [1] 3.96 1.06 2.93 2.49 2.11 1.26 4.61
```

Above, `val`

shows the seven points in parameter space at which we have run the code, and `d`

shows the output at those points. Now suppose we wish to know what the code would have produced at point \(p=(0.5, 0.5, 0.5)\), at which the point has not actually been run. This is straightforward with the package:

```
p <- c(0.5,0.5,0.)
fish <- c(1,1,4)
A <- corr.matrix(val,scales=fish)
interpolant(p, d, val, A = A, scales=fish, give=TRUE)
#> $betahat
#> const alpha beta gamma
#> -0.363 1.221 1.905 3.072
#>
#> $prior
#> [,1]
#> [1,] 1.2
#>
#> $beta.var
#> const alpha beta gamma
#> const 0.995 -0.510 -0.184 -0.713
#> alpha -0.510 0.950 -0.275 0.172
#> beta -0.184 -0.275 0.914 -0.192
#> gamma -0.713 0.172 -0.192 1.524
#>
#> $beta.marginal.sd
#> const alpha beta gamma
#> 0.997 0.975 0.956 1.234
#>
#> $sigmahat.square
#> [1] 0.64
#>
#> $mstar.star
#> [,1]
#> [1,] 1.42
#>
#> $cstar
#> [1] 0.165
#>
#> $cstar.star
#> [1] 0.2
#>
#> $Z
#> [1] 0.358
```

Above, object `fish`

is a vector of roughness length (“scales”) corresponding to the small-scale covariance properties of our function. This may be estimated from the problem or from the datapoints. Matrix `A`

is a normalized variance-covariance matrix for the points of `val`

.

The output gives various aspects of the Gaussian process associated with the original observations. The most interesting one is `mstar.star`

which indicates that the best estimate for the code’s output, if it were to be run at point \(p\), would be about 2.41.

R. K. S. Hankin 2005. “Introducing `BACCO`

, an R bundle for Bayesian analysis of computer code output”. *Journal of Statistical Software*, 14(16)