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

[John Denker <jsd@av8n.com>]

On 9/21/21 10:28 AM, Paul Nord wrote:

> 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?

On 9/22/21 8:14 AM, Paul Nord wrote:

> Traditionally we have them fit a double exponential function to this data.
> But this is fraught with problems and subtle choices in the analysis which
> will change the result.

There are subtle choices that even precede the analysis step,
including those mentioned in question 1 above.

Here's a related question, even simpler:

Suppose Alice uses a large number of short windows, and Bob
uses a small number of large windows. Will they get the same
result?  Even worse, suppose they switch horses in midstream,
switching from long to short window. How badly does that bias
the results? What weighting factors should be applied to the
long and short windows?

I encourage you to think about this a little bit, but don't
bother with guessing or with hand-wavy arguments, because that
will almost certainly get the wrong answer.

It's ridiculously easy to /calculate/ the right answer.

1) This can be used for testing your curve-fitting procedures.
 If your maximum-likelihood curve fit routine doesn't exhibit
 the correct invariance, it's broken.

2) This has major implications for experimental design.
 Summary: Short windows work fine.

The lurid details are spelled out here:
  https://www.av8n.com/physics/poisson-infer.htm#sec-long-short-invariance