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 02811944
ISRN LUTFD2/TFMS3149SE

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