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Re: [Phys-L] Bayesian Inference in Half-Life measurement

Oh, very interesting. I'll have to give pystan a try.

Paul


On Thu, Sep 23, 2021 at 3:26 AM Francois Primeau <fprimeau@uci.edu> wrote:

Paul,
If you are serious about considering the multiple sources of systematic
errors you list in your post, you might consider learning how to use the
probabilistic modeling language called Stan ( https://mc-stan.org/ ). It
allows you to define the prior probability density and likelihood function
in a pretty high-level language, which gets compiled so that Monte-Carlo
samples can be obtained from the posterior probability density. The
resulting code is fast, and it's easy to sample from some fairly high
dimensional probability densities. There is a bit of a spin-up to install
the software and learn to use it, but complicated models with tens to
hundreds of parameters can often be handled quite easily once you are up
and running. I have used it on a few geophysical inverse modeling
applications. Our probability models involved tens of nuisance parameters
that needed to be integrated over to obtain error bars on the processes of
interest. I believe the interface between Stan and R or Python is well
maintained, the one with Matlab, not so much.

Here is the blurb from the Stan website:

Stan is a state-of-the-art platform for statistical modeling and
high-performance statistical computation. Thousands of users rely on Stan
for statistical modeling, data analysis, and prediction in the social,
biological, and physical sciences, engineering, and business.
Users specify log density functions in Stan’s probabilistic programming
language and get:

- full Bayesian statistical inference with MCMC sampling (NUTS, HMC)
- approximate Bayesian inference with variational inference (ADVI)
- penalized maximum likelihood estimation with optimization (L-BFGS)

Stan’s math library provides differentiable probability functions &
linear
algebra (C++ autodiff). Additional R packages provide expression-based
linear modeling, posterior visualization, and leave-one-out
cross-validation.

Best,
Francois

On Wed, Sep 22, 2021 at 8:41 PM Paul Nord <Paul.Nord@valpo.edu> wrote:

bc,

Yes, the stability on the instrument over several days is another
systematic source of error.
Daily fluctuations in cosmic background is another. As are some very
subtle weather dependent changes in radon levels.

All good points. Still looking for the right way to extract the maximum
amount of information from the data without arbitrary choices in the
analysis.

Paul


On Wed, Sep 22, 2021 at 6:09 PM bernard cleyet <bernard@cleyet.org>
wrote:



On 2021/Sep/22, at 12:16, John Denker via Phys-l <
phys-l@mail.phys-l.org>
wrote:


We agree that "simply subtracting the background will sometimes
result in a negative number of counts".


That’s not the only problem.

If I understand correctly, if this is likely, that implies a rather
small
counting rate, and, therefore, long times counting will be done; unless
the
half life is too short. So long background counting, but the
background
changes, is it diurnal? Or? Another project.


Any way; In my v. long time counting, I find sig diffs with counting
background for 200 minutes [1] separated by six and/or twelve hours.
I’ve
considered counting the source and the background on two apparatuses.
(~
two inches of lead shielding)

As I’ve posted earlier this is “junk” collected in filters.


Also I’ve noticed that the decay of mBa-137? end in a higher
background
than the back. collected before adding the elution from the Cs-137
“cow”.
This is even after several days. So I conclude the separation using
the
(is it?) ion exchange resin is not perfect. Next project is to use my
SCA
to verify it’s Cs-137 “leakage”.


Later:
In an associated search, I find the Pasco version claims < 50 Bq/ml
leakage. I have an expensive dated calibrated Cs source, so I'll
calibrate one of my NaI detectors and verify. Maybe.


[1] The longest selected time on my The Nucleus 550 scaler-timer.


bc
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--
Professor of Earth System Science
Rm 3224 Croul Hall
University of California, Irvine
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Forum for Physics Educators
Phys-l@mail.phys-l.org
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