On Thu, May 8, 2008 at 12:02 PM, Charles R Harris <[EMAIL PROTECTED]> wrote: > > On Thu, May 8, 2008 at 10:56 AM, Robert Kern <[EMAIL PROTECTED]> wrote: >> >> On Thu, May 8, 2008 at 11:25 AM, Charles R Harris >> <[EMAIL PROTECTED]> wrote: >> > >> > On Thu, May 8, 2008 at 10:11 AM, Anne Archibald >> > <[EMAIL PROTECTED]> >> > wrote: >> >> >> >> 2008/5/8 Charles R Harris <[EMAIL PROTECTED]>: >> >> > >> >> > 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.
*YES*. As David pointed out, many of these PDFs are in exponential form. Most of the meaningful variation is in the exponent, not the mantissa. -- Robert Kern "I have come to believe that the whole world is an enigma, a harmless enigma that is made terrible by our own mad attempt to interpret it as though it had an underlying truth." -- Umberto Eco _______________________________________________ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion
