Description Usage Arguments Details Value Author(s) Examples

Set a covariance model for kriging the sample means of the involved statistics or for the variance matrix of the statistics.

1 2 3 |

`model` |
name of covariance model |

`param` |
numeric vector, |

`npoints` |
number of sample points already evaluated for covariance parameter estimation |

`var.sim` |
numeric vector, |

`nugget` |
starting value for (global) nugget variance estimation |

`trend` |
trend order ID: either linear (=1) or quadratic (=2) for polynomial trend terms |

`fixed.param` |
vector of names, corresponding to ' |

`lower` |
lower bounds of covariance parameters for REML estimation |

`upper` |
upper bounds of covariance parameters for REML estimation |

`...` |
additional arguments which can be stored |

The function defines a covariance model for kriging the sample mean values of an involved statistic. The covariance model
(including a polynomial trend) defines the spatial dependence between different locations (points) of the
parameter space. Currently, the function provides the generalized covariance models
('`sirfk`

', see `fitSIRFk`

) of order *k=1,2*
and the Mat*\textrm{\'{e}}*rn covariance model with scale (or sill) parameter '`scale`

', smoothness parameter
'`alpha`

', respectively, '`nu`

', and the range parameter '`rho`

' defined only for the latter. A power exponential
covariance model named "`powexp`

" is also supported.

If a vector of simulation variances is statically set by '`var.sim`

' for each location these are used as (local)
nugget variance estimations which account for the sampling variability due to the repeated measurements of the statistics
by simulation. The length should match the number of locations '`npoints`

' otherwise the given vector components
are recycled. A global scalar valued nugget, which can captures the variance of the underlying random function, can be set by
'`nugget`

' as a starting value for the REML estimation procedure. Clearly, both types of nugget variances have a direct
influence on the REML estimates.

The default starting parameters are set to `("scale"=0.001,"alpha"=1.5)`

for the '`sirfk`

' model. The
Mat*\textrm{\'{e}}*rn model uses the following parameters `("scale"=1.0,"nu"=2.5,"rho"=3.0)`

. The default
parameters for the power exponential covariance model are `"scale"=1.0`

, (isotropic) range parameter
`"phi"=1.0`

and power `"kappa"=1.5`

with *0<κ≤q 2*.
The corresponding lower and upper bounds are chosen such that the underlying random function remains
twice continuously differentiable. Further, setting the names of the covariance parameters in '`fixed.param`

',
excludes these parameters from subsequent REML estimations such that they remain unchanged.

The above settings are applicable for a wide range of statistics but, however, generally depend on the kind of statistics to be interpolated
and thus have to be chosen carefully. Note that a valid (generalized) covariance model for kriging requires at least *q+2* design points
for the trend order *k=1* and *1+(q+1)(q+2)/2* for *k=2* where *q* is the dimension of the unknown model parameter.

Object of class `covModel`

, a list of following elements

`model` |
integer of covariance function |

`param` |
estimtated covariance parameters |

`start` |
start point of REML estimation of covariance parameters |

`trend` |
trend order |

`fix.nugget` |
vector of (fixed) values used as local nugget variances |

`free` |
index of free parameters for REML estimation |

`lower` |
lower bounds of covariance parameters for REML estimation |

`upper` |
upper bounds of covariance parameters for REML estimation |

`...` |
additional objects which can be stored |

M. Baaske

1 2 | ```
# set the standards sirf-2 covariance model
setCovModel("sirfk",npoints=12)
``` |

mbaaske/qle documentation built on Feb. 3, 2018, 11:02 a.m.

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