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

[Brian Whatcott <betwys1@sbcglobal.net>]

Francois Primeau <fprimeau@uci.edu>To:phys-l@phys-l.orgCc:Phys-lWed, Sep 22 at 3:24 PM@Brian: I think your intuition is correct that if the decay rates are
sufficiently different, the "old school" method would work fine, provided
you collected data multiple times early on to resolve the decay of the
first isotope and then more data that are spaced further apart to resolve
the decay of the longer-lived isotope.

Now I'm curious to try it with simulated data and background noise to see
how well the individual decay rates can be estimated as the number of
counts gets small. The problem is that the posterior probability will be
over a 5-dimensional space, and doing the simple (and transparent)
discretization of the posterior over a regular mesh will become quite
expensive. So I might need to be smarter about how I marginalize out the
nuisance parameters, i.e., how I integrate over N1o, N2o, and B in the
joint posterior for (tau1, tau2, N1o, N2o, and B) to get a joint posterior
for tau1 and tau2 alone. It makes the problem less fun.

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I am way behind you Francois, but I did trim your script to a Cu half life of 12.7 hours nominal, and rather low startingactivities of either  4E4 hot atoms or 2E4 hot atoms and ran five trials on each.I was surprized with the variability of the results, without accounting for background or competing decay species.This is far removed from a student questionaire more like this:  A counter registers a rate of 982/min and 24 hours later, a rate of 244/min.What is the half-life (multiple choice)   <g>
Here is the plot in question for my assumptions:https://imgur.com/zt5YFCx