[Numpy-discussion] Log Arrays

[Warren Focke]

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.

w