Re: [Phys-L] Analysis of Half-Life measurement using PyStan

[Paul Nord <Paul.Nord@valpo.edu>]

Excellent observations, of course.  Using the pystan library code I'd
probably just give a narrow bound around the measured value.  They got
something near 17 counts per minute for the background.  I tried that just
now, it does give slightly better agreement with the accepted values.  And
the long half life has a SD of 14 minutes.  It would be interesting to see
if a time-varying background could be convincingly deduced from this data.
Or there may be some short-lived half life from some other atoms in the
sample (though copper is generally very pure because it is refined through
electroplating).  Maybe copper oxide... nope, Oxygen doesn't have much of a
thermal neutron cross section.  Anyway, there is probably not enough data
to try any other model comparison assessment.

I'm surprised you didn't find much of interest in the first 25 minutes of
MacKay's lecture.  He really critiques, or actually tears apart, everything
that physics majors are taught about data analysis.  We tell them,
"Everything is pretty much a gaussian, so just treat it that way."  And
then the first measurement we tell them to do is to take a caliper and
measure the width of a block.  Unless they bungle the measurement they'll
usually get a clear lower limit with a few stray points that are higher by
one or two digits in the smallest decimal place represented on the device.
I guess what I'm saying is that it's odd that we tell them that everything
is Gaussian when experience after experience shows them that it clearly is
not.

Paul


On Tue, Oct 12, 2021 at 5:28 PM John Denker via Phys-l <
phys-l@mail.phys-l.org> wrote:

> On 10/12/21 3:10 PM, I wrote:
> > You can shift a Gaussian left or
> > right and it's still a Gaussian. Not so with Poisson processes.
>
> To say the same thing in a little more detail:
>
> When people speak of Gaussians they are referring to a two-parameter
> family of distributions. You can shift the mean without changing the
> standard deviation and vice versa.
>
> The Poisson family is a *one* parameter family.
> You *cannot* change the mean without changing the standard deviation
> and vice versa.
>
> This is why you cannot "subtract" the background from the data side
> of the equation. You need to account for it by *adding* it (as a
> constant or otherwise) on the model side of the equation.
>
> Fitting routines don't always make it easy to pass non-adjustable
> parameters to the fitting function, but usually it is possible
> without rewriting the function code. Or just rewrite the code if
> you have to.
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