[Numpy-discussion] Log Arrays
Charles R Harris
Thu May 8 11:25:37 CDT 2008
On Thu, May 8, 2008 at 10:11 AM, Anne Archibald <firstname.lastname@example.org>
> 2008/5/8 Charles R Harris <email@example.com>:
> > What realistic probability is in the range exp(-1000) ?
> Well, I ran into it while doing a maximum-likelihood fit - my early
> guesses had exceedingly low probabilities, but I needed to know which
> way the probabilities were increasing.
The number of bosons in the universe is only on the order of 1e-42.
Exp(-1000) may be convenient, but as a probability it is a delusion. The
hypothesis "none of the above" would have a much larger prior.
But to expand on David's computation... If the numbers are stored without
using logs, i.e., as the exponentials, then the sum is of the form:
x_1*2**y_1 + ... + x_i*2**y_i
Where 1<= x_j < 2 and both x_i and y_i are available. When the numbers are
all of the same general magnitude you get essentially the same result as
David's formula by simply by dividing out the first value.
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