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SUMMARY:Are covariances meaningless in criteria for optimal designs for pr
ediction?
DTSTART:20220627T130000Z
DTEND:20220627T132000Z
DTSTAMP:20241007T201800Z
UID:indico-contribution-260@conferences.enbis.org
DESCRIPTION:Speakers: Helmut Waldl (Johannes Kepler University Linz)\n\nCl
assical optimality criteria for the allocation problem of experimental des
igns usually focus on the minimization of the variance of estimators.\nOpt
imal designs for parameter estimation somehow minimize the variance of the
parameter estimates. Some criteria just use the variances (A-optimality\,
E-optimality) whereas other criteria also implicitly consider the covaria
nces of the parameter estimates (D-optimality\, C-optimality).\nTraditiona
l criteria for optimal designs for prediction minimize the variances of th
e predicted values\, e.g. G-optimal designs minimize the maximum variance
of predictions or I-optimal designs minimize the average prediction varian
ce over the design space. None of these criteria consider the covariances
of the predictions.\nIf we want to control the variation of all (i.e. more
than just one of) the predictions we should think of measures for the ove
rall variation of a multivariate data set:\nThe so-called *total variation
* of a random vector is simply the trace of the population variance-covari
ance matrix. This is minimized with V-optimal designs.\nThe problem with t
otal variation is that it does not take into account correlations among th
e predictions. This is done by an alternative measure of overall variance\
, the so-called *generalized variance* introduced by Wilks 1932. The large
r the generalized variance the more dispersed are the data.\nThe generaliz
ed variance is defined as the determinant of the covariance matrix and min
imizing this determinant might serve as optimality criterion as well as ot
her related criteria based on the condition number of the covariance matri
x.\nThe different optimality criteria are compared by means of a computer
simulation experiment producing spatio-temporal data.\n\nhttps://conferenc
es.enbis.org/event/18/contributions/260/
LOCATION:EL5
RELATED-TO:indico-event-18@conferences.enbis.org
URL:https://conferences.enbis.org/event/18/contributions/260/
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