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

 Paul Nord <>>
  Wed, Sep 22 at 10:48 PM>> Brian,

You'd really enjoy David MacKay's lecture 10 on Information theory.  He
really rips into physicists regarding "old school" methods.  He's a
physicist, actually.  So he should know.

Basically, the "old school" method is wrong and is not used in modern
analysis of half-life measurements.

Paul,I did indeed enjoy David's lecture recordings, taken two years before his death from a stomach cancer. He was an Eng Professor at Cambridge who earlier visited CalTech as a Fullbright Scholar, where hisPhD thesis was to do with Bayesian neural net estimation.The following lecture #11 has a tantalizing glimpse of estimating two decay lifetimes via soft K meansdespite his visible nose holding at about 20 minutes into: ;
I was unable to replicate his graphs in Gnuplot from the data given here:

...because this gnuplot script has prerequisites, excluded from the lecture slide, but I noticedthe sciPython code version included in your mail did indeed  replicatethe Mackay graphs  after I downloaded WinPython with Spyder environment from:

I would be remiss not to mention a book of David's published with his own funds, and sold out in a week, called "Sustainable Energy - without the hot air" now available on line here:

Another pointer of yours,

gave a particularly clear step by step description into Bayesian probability estimation, I felt. The use of Fortran as the illustrative language added a certain whistful note to the lecture.I spotted this footnote:1 Davenport and Patil, in the Harvard Business Review, called the job of data scientist “the sexiest job of the 21stcentury”

I looked at what this epithet could mean by reading the lecture at this pointer: which is an introduction to graphical data science using R language,

....but did not tarry too long, even to explore a topic like "Why low quality diamonds are more expensive"concerning the dangers of misconstruing visual data.
I notice that another subject area is also growing like the flowers in Spring: Biology. (CRISPR, Gene editing, How to grow a Wooly Mammoth and all that.)  Here is a lectureon Bayesian probability from that perspective:

I was pleased to see that John Denker was moved to answer one of your two questions , Paul;the one about using narrow windows onto a decay process.   This provides some underpinningfor the sort of question that students are sometimes asked about decay like this:"What is the half life of an isotope with a recorded decay count of 12345 and twenty four hours later, a  count of 1234" - which amounts to much the same as two very narrow observation windows.
I liked best the Francois Primeau contributions which allowed me to easily generate data sets to checkthe accuracy of ignoring a short-lived contributor to a long decay set. As I expected, I could providea best fit value for Tau of the long lived species with 0.1 % accuracy by cutting out the front end data with the short-lived species, entirely. You know, this is the old-school protocol that reputedly doesn't work <g>.
I hope Francois will not mind my minor nitpick on his script which says

"tau_true = 52*60*60; %  half-life of neutron activated copper in seconds".
Tau is of course the mean lifetime or time constant of a count which falls to 1/e  times its initial value, not t1/2 which equals  ln2*tau.David Mackay too called Tau by the symbol lambda in his lectures. Lambda is sometimes used as the symbol for  decay rate, so that Co = C*exp( t/tau) or  C*exp(lambda*t) can both be found.
Finally, I see that Bayesian methods are no longer controversial after more than 200 years - so theymay even be regarded as 'just math'.