On Wed, 8 May 2002, Roy Malka wrote:
> I would highly appreciate any hint on estimation of
> conditional continuous probability density function,
> i.e., p(A|B) where A and B are continuous.
You're walking into a minefield here. The problem is that the definition
of the density p(A|B) depends on your limiting process. That is, p(A | B)
really means (using somewhat sloppy notation)
limit_{dB -> 0} P(A in a dA | B in b dB) / dA
You can get different numbers for the conditional density depending on how
you approach the limit. For example, consider a uniform density over the
sphere. Now consider the following:
p(latitutde = x | longitude = 0)
Is dB a ribbon of uniform width centered on the line of 0 longitude going
from south pole to north pole? Or does dB have the shape of an orange
segment, i.e., is it the set of all points with longitude in the range
[-epsilon, +epsilon], for some epsilon > 0? You will get quite different
numbers for the conditional probability density depending on which choice
you make.
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