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

[bernard cleyet <bernard@cleyet.org>]

Possibly the reason for few responses is such data doesn’t apply to a Bayesian analysis. 

Of course my understanding of using Bayesian stats. is minimal.  I see little difference in collecting decay data continuously over a long period and discontinuously as long as the counts are correctly time identified.  Ive been doing this for some time in an effort to identify the isotope(s) in Salinas Valley agricultural “dust” collected from window filters in my home.   

Of course, as more data is collected the half life will become more accurate, because the data observes a Poisson distribution.  

bc ….   doesn’t fear treading, and expects a final from JD.  and comment from AW.  

p.s.  Is PN  using the 10’ count as an average for a single datum point or, for example, ten one minute counts?   I’ve not interpreted the Python, as I don’t know Python, and only superficially C++, or for that matter, BASIC, Algol, and Fortran 2.


> On 2021/Sep/21, at 10:28, Paul Nord <Paul.Nord@valpo.edu> wrote:
>
> That title doesn't google well.  It seems like there should be a good
> reference for this.  The best I've got is David MacKay's code here:
> http://www.inference.org.uk/mackay/itprnn06/slides/10/mgp00010.html
> Translated into python below.
>
> Two questions:
> 1. If we record the number of counts observed with a geiger tube at
> discrete periods within the decay, is this approach still valid?  Say that
> I've got a sample with a 52 hour half life.  I come back about once a day,
> fire up the good old geiger tube and measure the activity for 10 minutes.
> Can I just use that number of counts as the power of a probability function
> to multiply through here?
>
> 2. Will this give me a good result if I'm extracting multiple decay periods
> from the same data?
>
> The half lives of neutron activated copper is the experiment, actually.
>
> Paul
>
>
> import matplotlib.pyplot as plt
>
> import numpy as np
>
> import math
>
>
> a = 1.0
>
> b = 20.0
>
>
> def p(x,l):
>
>    val = math.exp( -x/l ) / Z(l)/l
>
>    return val
>
>
> def Z(l):
>
>    val = math.exp( -a/l) - math.exp(-b/l)
>
>    return val
>
>
> def like(l):
>
>    return p(3,l) * p(5,l) * p(12,l)
>
>
>
> t1 = np.arange(0.01,1000.0,.1)
>
>
>
> fig,axs = plt.subplots(2)
>
> axs[0].semilogx()
>
> axs[1].semilogx()
>
>
> axs[0].plot(t1,[p(3,x) for x in t1])
>
> axs[0].plot(t1,[p(5,x) for x in t1])
>
> axs[0].plot(t1,[p(12,x) for x in t1])
>
>
> axs[1].plot(t1,[like(x) for x in t1])
>
>
> plt.show()
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