Far East Journal of Theoretical Statistics
Volume 7, Issue 1, Pages 19 - 33
(May 2002)
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A SYSTEM THEORETICAL CHARACTERIZATION OF THE RELATION BETWEEN
FISHER’S AND BAYES’ METHODS
Shiro Ishikawa (Japan)
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Abstract: Motivated by the great success of
von Neumann’s axiomatic approach to quantum mechanics, in this paper we
propose an axiomatic formulation of statistics in terms of measurements.
Simultaneously, we clarify the relation between Fisher’s and Bayes’ methods
as follows. In statistics, the information is described in two ways, i.e.,
Fisher’s method (in terms of likelihood quantities) and Bayes’ method (in
terms of weights). Further, we show that the two methods can be translated from
each other by the idea that the concept of "no information (i.e., the
situation after a shuffle)" must be common to both the methods. Thus we
conclude that Fisher’s and Bayes’ methods are different representations of
the same thing. In our approach we are not concerned with such argument as
"objective or subjective". |
Keywords and phrases: general system theory, measurement, Fisher’s method, Bayes’ method. |
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