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8. Decision theory and Geodesy
It is extremely unlikely that geodesy would be revolutionized if
all geodesists used the decision-theory approach to all their problems.
Previous and present generations of geodesists have used and are
using scientific insight and experience to make geodesy what it is
to-day, and it is preposterous to think that judgement cannot be
sound if it is perhaps not based on a completely specified model
(whose validity may be questionable anyway). The trouble is that
what is sound judgement or common sense to one geodesist may
be the opposite to another. In general, the scientific approach to
any problem distinguishes itself by a methodological, and, as far
as possible objective and quantitative analysis. It is vitally impor
tant for the solution of any decision problem to state clearly and
completely what actually the problem is; in this respect it will
help to be fully aware of the factors that enter into a decision
problem, and this is a quite general lesson one can learn from
decision theory.
More specifically, by the decision-theory approach the statistical
methods used by geodesists can be viewed from a more general
point of view, a point of view which in principle takes the conse
quences of decisions and their cost into account and thus stimulates
reflection upon the ultimate aim of activities. There can be no
doubt that a quantification of purposes is often very difficult in
geodesy. It is the same in general statistics. To quote K. A. Brown-
lee [2]"The practical usefulness of this (decision-theory) approach
has been hindered by the rareness with which one can actually
estimate with any confidence the cost functions Classical
statistical inference operates one stage further back from the
decision making process: Very roughly speaking it confines itself
to establishing what can be said about the facts of the situation,
and it leaves the decision as to what to actually do, if anything,
to the common sense of the experimenter."
We have already stated in par. 6 on testing hypotheses, that
often a specification of the action probabilities is as far as one can
go; the above quotation says essentially that further on one must
use his common sense, whatever that may be. In the case of para
meter estimation the corresponding situation is that one computes
the accuracy of estimatesthe acceptability of certain accuracies is
judged by common sense, experience or official tolerances. This
is a field known by every geodesist; everyone is familiar with
specifications of accuracies required, tolerances etc. But it is an
open question if some of these requirements have not been made
from a too narrowly geodetic point of view. There seem to be
examples where existing official tolerances have been made less
stringent to make possible the application of new techniques, e.g.
photogrammetry. Many tolerance specifications seem to be based
rather on what a reasonably good surveyor can get out of his
