Various intermediate expressions needed by the multivariate emulator

1 2 3 4 5 6 7 8 | ```
regressor(x,LoF)
beta_hat(expt,hp,LoF, ...)
betahat_mult(H, Sigmainv, d)
betahat_mult_Sigma(H, Sigma, d)
cstar(x1, x2=x1 , expt, hp, LoF = NULL, Sigmainv=NULL, ...)
eq2.36(H, Sigmainv, d, log=TRUE)
eq2.36_Sigma(H, Sigma, d)
var.matrix(x1,x2=x1,hp, ...)
``` |

`x,x1,x2` |
Objects of class |

`H` |
Matrix of regressors (create this with |

`d` |
Vector of observations, possibly not all of the same dimensions (eg some elements might be Kelvin, others millimeters of rain per year) |

`expt` |
Object of class |

`Sigma` |
The variance matrix of |

`log` |
Boolean, with |

`Sigmainv` |
The inverse of the variance matrix of |

`LoF` |
A list of functions with default |

`hp` |
Object of class |

`...` |
Extra arguments which are
passed (via |

Function `regressor()`

creates a (sort of) direct sum of
regressor matrices for an overall regressor matrix. It returns a
matrix whose rows are the regressor functions for each row in the
`df`

argument. Each type of observation has its own
‘slot’ of columns, the others being filled with zeros.

The emulator package *should* have used this method (rather than
messing about with `regressor.basis()`

and
`regressor.multi()`

).

To get the regression coefficients, the user should use function
`beta_hat()`

, which is the user-friendly version. It is a
wrapper for function `betahat_mult_Sigma()`

.

The equation for `var.matrix()`

is

*ommitted--see a LaTeXed file*

Robin K. S. Hankin

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | ```
data(mtoys)
H <- regressor(toy_mm, toy_LoF)
Sigma <- var.matrix(toy_mm, hp=toy_mhp)
Sigmainv <- solve(Sigma)
jj <- toy_mm_maker(34,35,36)
expt <- experiment(jj,obs_maker(jj,toy_mhp,toy_LoF,toy_beta))
x1 <- jj[c(20,40,100),]
xold(x1) <- 0.2
x2 <- jj[c(11,21:24,40:42),]
xold(x2) <- xold(x2)+0.1
#primary function of package:
multem(x=x1, expt, hp=toy_mhp, LoF=toy_LoF)
# conditional covariance matrix:
cstar(x1,x2, expt, hp=toy_mhp, LoF=toy_LoF)
``` |

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