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*From*: John Denker <jsd@av8n.com>*Date*: Tue, 12 Oct 2021 15:27:52 -0700

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.

**Follow-Ups**:**Re: [Phys-L] Analysis of Half-Life measurement using PyStan***From:*Paul Nord <Paul.Nord@valpo.edu>

**References**:**[Phys-L] re Bayesian Inference in Half-Life measurement***From:*Brian Whatcott <betwys1@sbcglobal.net>

**[Phys-L] Analysis of Half-Life measurement using PyStan***From:*Paul Nord <Paul.Nord@valpo.edu>

**Re: [Phys-L] Analysis of Half-Life measurement using PyStan***From:*Paul Nord <Paul.Nord@valpo.edu>

**Re: [Phys-L] Analysis of Half-Life measurement using PyStan***From:*John Denker <jsd@av8n.com>

**Re: [Phys-L] Analysis of Half-Life measurement using PyStan***From:*Paul Nord <Paul.Nord@valpo.edu>

**Re: [Phys-L] Analysis of Half-Life measurement using PyStan***From:*John Denker <jsd@av8n.com>

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