Confidence regions for local maxima and minima of surfaces reconstructed from finite data

Eva Sjö

Department of Mathematical Statistics,
Lund Institute of Technology,
Lund University,
1998

ISSN 0281-1944
ISRN LUTFD2/TFMS--3149--SE


Abstract:
There are several methods of surface reconstruction from a finite number of spatial data. The reconstruction is an estimate of the true surface, and it is often used to estimate topographical characteristics, e.g. to identify areas of extreme values. The uncertainty of an estimate depends both on uncertainties introduced by the reconstruction and on observation errors.
We present a method to approximately evaluate the reliability of the estimates of the locations of local maxima (or minima) of the true surface. The true surface is modeled as a continuous parameter Gaussian random field, and the reliability is presented as confidence regions around the local maxima of the reconstruction.
The method applies for general finite dimension of the spatial parameter, and for any reconstruction method that gives a differentiable surface with an explicit covariance function as result.
Key words:
Gaussian random field, local maximum, confidence region, surface reconstruction