Re: Anybody know how to calculate this condiditonal Probability ?


Xufei.Wang@xxxxxxxxx wrote:
Dears

If P (Qt | Q, fi), (i=1,2,....,n), have been separately calculated,
How to calculate the probability distribution of P (Qt | Q, f1,
f2...fn)?
Is it just simply the sum of P (Qt | Q, fi)?
Or in more complicated way?

Is it depends on the relationship of the factors fi, f2... fn?
More information is needed for the calculation?

Yes, you need more information in general. Look at the case with just
two
f's, call them f and g. Then

P(Qt | f, g, Q) = P(Qt, f, g | Q) / P(f, g | Q) .

Now we can perhaps assume that f and g are independent of Q and of each
other:

P(Qt | f, g, Q) = P(Qt, f, g | Q) / (P(f) P(g)) .

Now,

P(Qt, f, g | Q) = P(g | Qt, f, Q) P(Qt, f | Q)

= P(g | Qt, f, Q) P(Qt | f, Q) P(f) .

Now *if*

P(g | Qt, f, Q) = P(g | Qt, Q) = P(Qt | g, Q) P(g) / P(Qt | Q) , (1)

where

P(Qt | Q) = \int dg P(Qt | g, Q) P(g) ,

then

P(Qt | f, g, Q) = P(Qt | f, Q) P(Qt | g, Q) / P(Qt | Q) .

The assumption, equation (1), that we know nothing about g if we know
Q,
Qt, and f, is almost certainly false. Indeed almost the opposite is
true:
if we know Q, Qt, and f, we may know g exactly. This is why, as I said
in
my previous post, you need to analyse the physics of the situation, to
know
how f and g together affect the irradiation. Knowing how they do it
separately is not enough. Now maybe they do not affect one another in
some
sense, but maybe they do. Probability cannot tell you this.

illywhacker;

.

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