[Numpy-discussion] Log Arrays
Charles R Harris
charlesr.harris@gmail....
Thu May 8 13:00:28 CDT 2008
On Thu, May 8, 2008 at 11:31 AM, Warren Focke <focke@slac.stanford.edu>
wrote:
>
>
> On Thu, 8 May 2008, Charles R Harris wrote:
>
> > On Thu, May 8, 2008 at 10:11 AM, Anne Archibald <
> peridot.faceted@gmail.com>
> > wrote:
> >
> >> 2008/5/8 Charles R Harris <charlesr.harris@gmail.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.
>
> You might like to think so. Sadly, not.
>
> If you're doing a least-square (or any other maximum-likelihood) fit to
> 2000
> data points, exp(-1000) is the highest probability you can reasonably hope
> for.
> For a good fit. Chi-square is -2*ln(P). In the course of doing the fit,
> you
> will evaluate many parameter sets which are bad fits, and the probablility
> will
> be much lower.
>
> This has no real effect on the current discussion, but:
>
> The number of bosons in the universe (or any subset thereof) is not
> well-defined. It's not just a question of not knowing the number; there
> really
> is no answer to that question (well, ok, 'mu'). It's like asking which
> slit the
> particle went through in a double-slit interference experiment. The
> question is
> incorrect. Values <<1 will never be tenable, but I suspect that the minus
> sign
> was a typo. The estimates I hear for the number of baryons (protons,
> atoms) are
> ~ 1e80.
>
Say, mostly photons. Temperature (~2.7 K) determines density, multiply by
volume. But I meant baryons and the last number I saw was about 1e42.
Chuck
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