Hi Cliff,
> BG> One thing that complicates the problem is that ,in some > cases, as well as > BG> inferring probabilities one hasn't been given, one may want to make > BG> corrections to probabilities one HAS been given. For > instance, sometimes > BG> one may be given inconsistent information, and one has to choose which > BG> information to accept. > > If I'm following this, this corresponds in your second statement to > the random point selection leading to *approximations* of > probabilities, Actually, in the rectangles test, we will never have inconsistencies, unless we specifically add noise to the data. Sorry if I made a mis-statement there. On the other hand, in real-world inference problems, one often has inconsistencies. For instance, in data loaded from biology databases, there may be inconsistencies due to errors in some of the databases. Similarly, in data loaded from sensors, there may be inconsistencies due to erroneous perceptions by one or another sensor (and the system may not know which is erroneous in a given case). > So don't we, in order to make assessments of the accuracy of the > approximations need to know the number of samples taken and have some > given confidence level of the randomness of the sampling process? That would be nice, but in real inference examples this kind of information is usually not available. > Somehow I see this ending up as finding a set a bell curves (i.e. > their height, spread and optimum) for each estimate. That is to say I > don't see *just* the probability as relevant but the probability > distribution...if I sample 10 people, the curves are all "wider" than > if I sample 100 people out of a 1,000 total. You can do that, it's true. One option we prototyped in Novamente was using "probability distribution truth values" instead of simple probability truth values. However, it vastly increases the computational cost, and in many cases there's not enough data to support a distributional truth value meaningfully. So the system is designed to be able to switch between distributional and simple truth values adaptively ;-) However, a truth value distribution need not be a bell curve. For example, how about the truth value of P( male | human ) As a number it's .5 As a distribution, it's bimodal, not Gaussian at all.... -- Ben ------- To unsubscribe, change your address, or temporarily deactivate your subscription, please go to http://v2.listbox.com/member/?[EMAIL PROTECTED]
