[Frost] Simple Q-factor example

[Derek Glazier]

Hi Michael
   Apologies if I have missed the point of the discussion. I think the 
behaviour observed in your nice analysis is what would be expected.
   The Q-factor explicitly requires inclusion of all variables that will 
be used in further analysis, so in your case certainly phi must be 
included in the nearest neighbours search. For other reactions also 
involving fits to decay angles for example, these decay angles must also 
be included in the nearest neighbour search.
   If this is not done then it is probably not actually the Q-factor 
method that is being applied but just a single probabilistic weight 
function for all events. So if the signal and background ratio change as 
a function of the variable you are interested in, clearly the single 
probabilistic weight function will not apply at all values of the 
variable. Instead the Q-factor is equivalent to making many 
probabilistic weight functions for events in very small bins of phi so 
the signal/background is approximately constant for that bin. This also 
has the implication that if the range of your phi bin for N nearest 
neighbours is large (e.g. if you have low statistics, or many variables) 
Q-factor will not work so well.
   Sorry if this adds to any confusion, but in short I agree with your 
analysis.
Cheers
Derek

On 11/08/16 23:38, Michael Dugger wrote:
>
> Hi,
>
> During our discussion today, regarding the
> Q-factor dependence on azimuthal angle, it
> became clear that I needed to have a better
> explanation. I have created an example that
> I hope illustrates the point I was trying
> to make.
>
> A simple Q-factor example can be found at
>
> https://userweb.jlab.org/~dugger/omega/omega6.pdf
>
> Note: The 2nd slide is just a repeat of what
> I had shown previously. The new information starts
> on slide 3.
>
> In addition, I have attached the plot
> (allCos.png) that Barry requested (moment method
> for integrated polar angle).
>
> Take care,
> Michael
>
>
>
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