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

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

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()