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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Optimal design and properties of correlated proces
ses with semicontinuous covariance - Stehlk\, M (J
ohannes Kepler Universitt)
DTSTART;TZID=Europe/London:20110721T153000
DTEND;TZID=Europe/London:20110721T161500
UID:TALK32117AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/32117
DESCRIPTION:Semicontinuous covariance functions have been used
in regression and kriging by many authors. In a r
ecent work we introduced purely topologically defi
ned regularity conditions on covariance kernels wh
ich are still applicable for increasing and infill
domain asymptotics for regression problems and kr
iging. These conditions are related to the semicon
tinuous maps of Ornstein Uhlenbeck Processes. Thus
these conditions can be of benefit for stochastic
processes on more general spaces than the metric
ones. Besides\, the new regularity conditions rela
x the continuity of covariance function by conside
ration of a semicontinuous covariance. We discuss
the applicability of the introduced topological r
egularity conditions for optimal design of random
fields. A stochastic process with parametrized mea
n and covariance is observed over a compact set. T
he information obtained from observations is measu
red through the information functional (defined on
the Fisher information matrix). We start with dis
cussion on the role of equidistant designs for the
correlated process. Various aspects of their pros
pective optimality will be reviewed and some issue
s on designing for spatial processes will be also
provided. Finally we will concentrate on relaxing
the continuity of covariance. We will introduce th
e regularity conditions for isotropic processes wi
th semicontinuous covariance such that increasing
domain asymptotics is still feasible\, however mor
e flexible behavior may occur here. In particular\
, the role of the nugget effect will be illustrate
d and practical application of stochastic processe
s with semicontinuous covariance will be given. \n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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