Yes, Probability theory exists
But "probability" is an important idea all by itself. What is the probability of a traffic accident at 12th and Main streets in given weather, for example. College courses about how to calculate probability are widely taught. I'm trying to point out the article's title is "Probability" and that "Probability Theory" would be better presented later in the article, or as its own article. Terry E. Olsen 18:40, 1 May 2007 (CDT)
In the "Example of the Bayesian viewpoint" section, it needs to be mentioned that the die is to be thrown more than once and that one is willing to consider the possibility that it is an unfair die, i.e. that the result on one roll may not be statistically independent of the result on another roll. Is this really a valid representation of how Bayes viewed probability, or is it a later construct loosely based on Bayes' views?
Under "Objective probability" it says "If our (empirical) results seem improbable, we may decide to do experiments to re-measure the "propensities"." This sounds to me like the Bayesian viewpoint, not the objective viewpoint. I think that in the objective viewpoint, if you have decided what your propensities are and you get some results -- well, those are your results and that's that. If you're going to go re-measuring your propensities that suggests that you had a prior probability that the original measured propensities were wrong. --Catherine Woodgold 10:53, 6 May 2007 (CDT)
I think the current version is not well thought out. Some complaints:
- In the "Bayesian probability" section:
- Contrasting "Conditional" and "Ordinary" is confusing in this context, since this distinction basically exists only in non-Bayesian theory.
- Also, the vague reference to "something much more specific and precise" needs to be made more specific and precise :-)
- In the "Example of the Bayesian viewpoint" section:
- The whole section seems rather difficult to comprehend, full rewrite necessary.
- In the "Frequentist probability" section:
- Short and sweet, but maybe more could be said?
- The main point of the "frequentist" is that probability is an inherent property of the object, one that we physically measure using statistics. This doesn't come out very clearly.
- In the "Example of the frequentist viewpoint" section:
- "Truly random" is a concept that should be avoided.
- Statistical estimation of parameters is referred to, but not mentioned explicitly.
- In the "The Axiomatic Approach" section:
- It's not really obvious what's meant by "Neither the Bayesian or the frequentist approach really tells us how to compute probabilities".
- The section needs to point out that probability theory is just a piece of math that can be used to model phenomena in the real world.
- In the "Example of the axiomatic approach" section:
- Not a very good example, as it doesn't draw heavily on axiomatics at all.
Ragnar Schroder 21:35, 28 June 2007 (CDT)