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

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

I was hoping for some feedback on this analysis.  Specifically, what did
you think of my conclusion:
"All of these models generate curves which are very close to the data.
While the errors seem very large, they are actually a better representation
of the true uncertainty in applying this model to this data.  Many
least-squares fitting functions will give uncertainties which give too much
confidence in the model predictions."

Paul


On Fri, Oct 8, 2021 at 3:07 PM Paul Nord <Paul.Nord@valpo.edu> wrote:

> I did a thing:
> https://sites.google.com/valpo.edu/double-exponential-decay/
>
> Surprisingly, the resulting uncertainties are bad while the fit looks
> quite good.  I've read that this sort of analysis gives a better estimation
> of the true uncertainty than one often gets with least squares fitting.
> Plotting a selection of 1000 models generated from this analysis shows that
> they all lie very close to the mean.  The assumptions of this model do not
> constrain the model parameters given the particular data collected.
>
> Said again: any of the terms in this model can be adjusted about 10%. You
> can still get a similar and reasonable fit.  You just need the right
> tweaking of the other parameters.
>
> Bad model assumptions here almost certainly include:
>   A) The background rate is constant
>   B) The stability of the detector
>
> Paul