For a quick walk through of various prob. theories, you may consult "The
Cambridge Dictionary of Philosophy." pp.649-651.
Basically, propensity theory is to deal with the problem that frequentist
prob. cannot be applied to a single case. Propensity theory defines prob.
as the disposition of a given kind of physical situation to yield an
outcome of a given type.
The following is extracted from one of my papers. It brielfy talks about
the history of classical theory, Reichenbach's frequentism and Fisherian
school:
------------
Fisherian hypothesis testing is based upon relative frequency in long
run. Since a version of the frequentist view of probability was developed
by positivists Reichenbach (1938) and von Mises (1964), the two schools
of thoughts seem to share a common thread. However, it is not necessarily
true. Both Fisherian and positivist's frequency theory were proposed as
an opposition to the classical Laplacean theory of probability. In the
Laplacean perspective, probability is deductive, theoretical, and
subjective. To be specific, this probability is subjectively deduced from
theoretical principles and assumptions in the absence of objective
verification with empirical data. Assume that every member of a set has
equal probability to occur (the principle of indifference), probability
is treated as a ratio between the desired event and all possible events.
This probability, derived from the fairness assumption, is made before
any events occur.
Positivists such as Reichenbach and von Mises maintained that a very
large number of empirical outcomes should be observed to form a reference
class. Probability is the ratio between the frequency of desired outcome
and the reference class. Indeed, the empirical probability hardly concurs
with the theoretical probability. For example, when a dice is thrown, in
theory the probability of the occurrence of number "one" should be 1/6.
But even in a million simulations, the actual probability of the
occurrence of "one" is not exactly one out of six times. It appears that
positivist's frequency theory is more valid than the classical one.
However, the usefulness of this actual, finite, relative frequency theory
is limited for it is difficult to tell how large the reference class is
considered large enough.
Fisher (1930) criticized that Laplace's theory is subjective and
incompatible with the inductive nature of science. However, unlike the
positivists' empirical based theory, Fisher's is a hypothetical infinite
relative frequency theory. In the Fisherian school, various theoretical
sampling distributions are constructed as references for comparing the
observed. Since Fisher did not mention Reichenbach or von Mises, it is
reasonable to believe that Fisher developed his frequency theory
independently. Backed by a thorough historical research, Hacking (1990)
asserted that "to identify frequency theories with the rise of positivism
(and thereby badmouth frequencies, since "positivism" has become
distasteful) is to forget why frequentism arose when it did, namely when
there are a lot of known frequencies." (p.452) In a similar vein, Jones
(1999) maintained that "while a positivist may have to be a frequentist,
a frequentist does not have to be a positivist."
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Chong-ho (Alex) Yu, Ph.D., MCSE, CNE
Academic Research Professional/Manager
Educational Data Communication, Assessment, Research and Evaluation
Farmer 418
Arizona State University
Tempe AZ 85287-0611
Email: [EMAIL PROTECTED]
URL:http://seamonkey.ed.asu.edu/~alex/
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