Dear Rolf, (sorry for the short reply, I am lacking time) At 18:23 01/07/2003, Rolf Haenni wrote: >Isn't it beautiful to see how switching from probabilities of events to >probabilities of provability of events allows to easily cope with such >incomplete models. How would you do it using flat densitiy functions >(Charles) or probability intervals (Marco)?
I am not advocating the use of probability intervals in general, I mentioned them to make my point clearer. I am for coherent lower previsions = sets of probability distributions (also called imprecise probabilities). This theory is more general than probability intervals and belief functions (interpreted as lower envelopes of distributions, unlike in the D-S theory of evidence), and is based on coherence requirements similar to the Bayesian case. (A comparison with other popular theories of uncertainty is in: Walley, P., 1996. Measures of uncertainty in expert systems. Artificial Intelligence 83(1), 1--58). Regarding ways to model prior ignorance with categorical random variables and imprecise probabilities, the point is very well made in a nice paper: Walley, P., 1996. Inferences from multinomial data: learning about a bag of marbles. J. Roy. Statist. Soc. Ser. B 58, 3--57. This paper clarifies many aspects of the prior ignorance problem, and may be interesting also to those not involved in imprecise probabilities. It also proposes the imprecise Dirichlet model. Best wishes, Marco
