setCovModel: Set a covariance model

Description Usage Arguments Details Value Author(s) Examples

View source: R/covariance.R

Description

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

Usage

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setCovModel(model = "sirfk", param = NULL, npoints = 0, var.sim = NULL,
  nugget = 0.00015, trend = 2, fixed.param = NULL, lower = NULL,
  upper = NULL, ...)

Arguments

model

name of covariance model

param

numeric vector, NULL (default), starting values of covariance parameters for estimation

npoints

number of sample points already evaluated for covariance parameter estimation

var.sim

numeric vector, NULL (default), local simulation variances (so-called local nugget variances)

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 'param' of covariance parameters, which are hold fixed for covariance parameter estimation

lower

lower bounds of covariance parameters for REML estimation

upper

upper bounds of covariance parameters for REML estimation

...

additional arguments which can be stored

Details

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.

Use of simulation variance

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.

Default parameters

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.

Value

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

Author(s)

M. Baaske

Examples

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

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