[Numpy-discussion] Log Arrays
Charles R Harris
Thu May 8 12:02:19 CDT 2008
On Thu, May 8, 2008 at 10:56 AM, Robert Kern <email@example.com> wrote:
> On Thu, May 8, 2008 at 11:25 AM, Charles R Harris
> <firstname.lastname@example.org> wrote:
> > On Thu, May 8, 2008 at 10:11 AM, Anne Archibald <
> > wrote:
> >> 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.
> When you're running an optimizer over a PDF, you will be stuck in the
> region of exp(-1000) for a substantial amount of time before you get
> to the peak. If you don't use the log representation, you will never
> get to the peak because all of the gradient information is lost to
> floating point error. You can consult any book on computational
> statistics for many more examples. This is a long-established best
> practice in statistics.
But IEEE is already a log representation. You aren't gaining precision, you
are gaining more bits in the exponent at the expense of fewer bits in the
mantissa, i.e., less precision. As I say, it may be convenient, but if cpu
cycles matter, it isn't efficient.
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