setCovModel: Set a covariance model

In qle: Simulation-Based Quasi-Likelihood Estimation

Description

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

Usage

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: 'sirfk' (default), 'matern', 'powexp', 'exp'
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 (as local nugget variances)
nugget	starting value for (global nugget) variance estimation
trend	integer, =2 (default) number of polynomial trend order: either set to linear (=1) or quadratic (=2)
fixed.param	vector of names, corresponding to 'param' of covariance parameters, which will be hold fixed for covariance parameter estimation by REML
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 the kriging approximation of the sample mean values of a summary statistic. The covariance model (which might include 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 (i.e. sill) parameter 'scale', smoothness parameter 'alpha', respectively, 'nu', and the range parameter 'rho' defined only for the latter and the (power) exponential covariance model 'powexp'.

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 simulations. The length should match the number of locations 'npoints' otherwise the given vector components are recycled to the number of 'npoints'. A global nugget value, which captures the variance of the underlying random function, could be set by 'nugget' as a starting value for the REML estimation procedure for covariance estimation. Clearly, both types of nugget variances have a direct influence on the REML estimates in terms of smoothness and goodness-of-fit.

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 these are hold fixed and used as given in the starting parameter.

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 'param'.

Value

Object of class covModel as a list of the following objects

model	integer number of covariance function
param	estimtated covariance parameter vector
start	start point for REML estimation of covariance parameters
trend	trend order number
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

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

qle documentation built on May 2, 2019, 9:55 a.m.