[Numpy-discussion] Log Arrays

[Gael Varoquaux]

On Thu, May 08, 2008 at 10:04:28AM -0600, Charles R Harris wrote:
>    What realistic probability is in the range exp(-1000) ?

I recently tried to do Fisher information estimation of a very noisy
experiment. For this I needed to calculate the norm of the derivation of
the probability over the entire state space as a function of a hidden
parameter. My probabilities where in most of the phase space very small,
and calculating the derivative in these regions was very numerically
unstable. However I could not drop these regions as they where
contributing significantly to the Fisher information. I could never get
clean results (everything was very noisy) and I gave up.

This was just to say that extremely small numbers, and their difference,
can be very significant, and that there is a strong usecase for
logarithmic operations (actually I should probably have worked a bit on
my formulas to express them all in logarithm form, but I ran out of
time).

Gaël