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guslI had seen this paper before, but I didn't realize that it echoed my feelings so well.
But here is a direct attack:
In Defense of Probability
Peter Cheeseman, SRI International
Abstract
In this paper, it is argued that probability theory, when used correctly, is sufficient for the task of reasoning under uncertainty. Since numerous authors have rejected probability as inadequate for various reasons, the bulk of the paper is aimed at refuting these claims and indicating the sources of error. In particular, the definition of probability as a measure of belief rather than a frequency ratio is advocated, since a frequency interpretation of probability drastically restricts the domain applicability. Other sources of error include the confusion between relative and absolute probability, the distinction between probability and the uncertainty of that probability. Also, the interaction of logic and probability is discussed and it is argued that many extensions of logic, such as ``default logic'' are better understood in a probabilistic framework. The main claim of this paper is that the numerous schemes for representing and reasoning about uncertainty that have appeared in the AI literature are unnecessary -- probability is all that is needed.
But here is a direct attack:
Let Many Flowers Bloom: A Response to "An Inquiry into Computer Understanding"
Joseph Y. Halpern
1 Approaches to uncertainty
Cheeseman makes a number of strong statements in Inquiry and Defense. Perhaps the most important of them can be summarized by the following two claims: (1) all the information we have about a situation about which we want to reason can be best represented in terms of probabilities, and (2) if we get new information, we should use Bayes' rule of conditioning to update our earlier probabilities.
Probability is a good method for representing uncertainty. I consider it to be the best (and certainly the best understood!) of all the methods currently available. I suspect it will end up being the method of choice for many applications. Indeed, I believe that many of the other methods proposed for reasoning under uncertainty can be best understood in terms of probability theory. (See, for example, [HF89] for some discussion and further references on the issue of how the DempsterÂShafer approach can be understood in terms of probability theory; see [Gro86, Hec86] for a discussion of how MYCIN's certainty factors can be understood in terms of probability theory.) However, it does not follow that probability should be the method of choice for every application (or for all parts of any one application).
Even if one is firmly committed to using probability theory, one does not have to be a Bayesian. There are many problems with the Bayesian position espoused by Cheeseman, mainly stemming from the question of how to assign probabilities and how they can be computed. Since these issues have been discussed at length in the literature, I will just briefly review them here. ...