[Gate-users] statistical uncertainty

[David Freese]

Not sure if someone has answered already, but I would probably treat the
number of scattered events and number of true events as Poisson random
variables.  Being Poisson, I would report the error for each as the square
root of the total number of counts, so you have:

scatter +/- sqrt(scatter)
trues +/- sqrt(trues)

Then dividing for the scatter fraction you add the relative errors in
quadrature:

scatter fraction  =  scatters / trues +/- sqrt ( (sqrt(scatter) / scatters)
^ 2 + (sqrt(trues) / trues)^2)
scatter fraction  =  scatters / trues +/- sqrt ( 1 / scatters + 1 / trues )


This is how I would report it.  If others have different methods, I would
also appreciate hearing those.


On Fri, Oct 20, 2017 at 6:22 AM, Amir Ghabrial <eng_amir_shawky at hotmail.com>
wrote:

>
> Dear GATE Users,
>
>
>
> * I am simulating PET scanner, and I am trying to calculate the scatter
> fraction statistical uncertainty as every time I do the simulation, I get
> different results, so I was wondering what is the right way to calculate
> the statistical uncertainty?. It would be much appreciated if somebody
> could point me in the right direction or share his experience about
> uncertainty calculation!  *
>
> *Thank you for your time and Considerations*
> *Kind regards,*
>
>
> *Amir Ghabrial PhD Research Student*
> *IEEE Member *
> *# 93954848 *
>
> *Faculty of Engineering and IT University of Technology Sydney*
>
> *Centre for Real-Time Information Networks *
> *Address: Building 11, Level 8, Room 218, Desk 11, *
> *15 Broadway, Ultimo NSW 2007*
>
> *Australia **Phone: 0415320349*
>
>
>
>
>
>
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