Re: [Phys-L] Analysis of Half-Life measurement using PyStan

[John Denker <jsd@av8n.com>]

On 10/12/21 3:10 PM, I wrote:
> You can shift a Gaussian left or
> right and it's still a Gaussian. Not so with Poisson processes.

To say the same thing in a little more detail:

When people speak of Gaussians they are referring to a two-parameter
family of distributions. You can shift the mean without changing the
standard deviation and vice versa.

The Poisson family is a *one* parameter family.
You *cannot* change the mean without changing the standard deviation
and vice versa.

This is why you cannot "subtract" the background from the data side
of the equation. You need to account for it by *adding* it (as a
constant or otherwise) on the model side of the equation.

Fitting routines don't always make it easy to pass non-adjustable
parameters to the fitting function, but usually it is possible
without rewriting the function code. Or just rewrite the code if
you have to.