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Re: [Phys-L] Half-Life measurement






John Denker via Phys-l <phys-l@mail.phys-l.org>UnsubscribeTo:phys-l@phys-l.orgCc:John Denker
Thu, Oct 14 at 7:56 PM
Addendum to previous message:Here is what the fits look like:  https://www.av8n.com/copper-decay/img48/rate-v-short-time-1.png ; https://www.av8n.com/copper-decay/img48/rate-v-long-time-1.pngor equivalently  https://www.av8n.com/copper-decay/pdf/rate-v-short-time-1.pdf ; https://www.av8n.com/copper-decay/pdf/rate-v-long-time-1.pdf
This is pretty much what you expect to see when fitting tonoisy data.
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The two plots John gave above were plotted from data in his previous message. This mentioned two datasets: "my_data" and "sean_data". I am not sure which data developed the plots. The iterative quadratic approximation method he used in lopt provided the following estimates.5.587 min for the shorter half life + 9% high  )13.68 hrs for the longer half life  + 7.7% high) Background rate was 12.7 counts/min          )   using  my_data (not sure if he incorporated Pauls corrected values around 3 minutes)
5.264 min for the shorter half life was +2.8% high )13.67 hrs for the longer half life was 12.1% high  ) Background rate was  14.35 counts/min               ) using Sean_data 
This nlopt routine does not appear to use Bayesian probability estimates, but I think John mentioned using published values of half lives for his initial iteration.( what I called brute force Bayesian in my  estimates)
These compare well with Paul Nord's Bayesian estimates below:
4.67 min for the shorter half life was 8.8% low        )12.76 hrs for the longer half life was 0.5% high (!)   )Background rate was 13.995 counts/min                 ) using my_data 

So far so good! Finally,  I admit to some puzzlement about the plots which John provided. 
When I digitized his plots I found the Short tau was 8.74 min, 6.06 min half life which is 18% highand the long tau was 8.05 hrs, half life 5.58 hrs was extremely low at -56%The background rate also seemed very high.    Not sure how I could stray so far from his good data.