We must warn the reader about another semantic confusion which has caused error and controversy in probability theory for many decades. It would be quite wrong and misleading to call
g(f)the ‘posterior distribution of
f’, because that verbiage would imply to the unwary that f itself is varying and is ‘distributed’ in some way. This would be another form of the mind projection fallacy, confusing reality with a state of knowledge about reality. In the problem we are discussing,
fis simply an unknown constant parameter; what is ‘distributed’ is not the parameter, but the probability. Use of the terminology ‘probability distribution for
f’ will be followed, in order to emphasize this constantly.
Of course, nothing in probability theory forbids us to consider the possibility that
fmight vary with time or with circumstance; indeed, probability theory enables us to analyze that case fully, as we shall see later. But then we should recognize that we are considering a different problem than the one just discussed; it involves different quantities with different states of knowledge about them, and requires a different calculation. Confusion of these two problems is perhaps the major occupational disease of those who fool themselves by using the above misleading terminology. The pragmatic consequence is that one is led to quite wrong conclusions about the accuracy and range of validity of the results.
- Jaynes, E. T. (2003-04-10). Probability Theory: The Logic of Science: Principles and Elementary Applications Vol 1 (Kindle Locations 4141-4147). Cambridge University Press. Kindle Edition.