What Can Be Learned from Signal vs. Background Efficiency Plots?

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The discussion focuses on interpreting signal vs. background efficiency plots, specifically the relationship between background efficiency and signal efficiency. It emphasizes that each point on the curve represents a different selection strategy, illustrating the trade-offs between retaining signal events and minimizing background events. An example is provided, showing how varying selections can lead to different efficiencies, highlighting the importance of optimizing these selections for better performance. The use of tools like TMVA for continuous selection is mentioned, which helps in generating the efficiency curves. Understanding these plots is crucial for improving event selection in data analysis.
ChrisVer
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What information can one obtain from the plots of the background vs signal efficiency? \epsilon_{bkg}(\epsilon_{sig})?
In particular I attach some plots I made by hand and I want to understand how to obtain what each tells us.
 

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Your plot should have 1/(background efficiency) or 1-(background efficiency) as vertical axis.

Each point on the curve is a possible selection. As an example, you can randomly take 60% of the events, then you have 60% signal efficiency and keep 60% of the background. That is not a good selection, of course. Your actual one might keep 90% of the signal events and keep only 5% of the background. If you make the selection a bit looser, you get 91% of the signal, but 10% of the background. Make this in a continuous way (with TMVA usually) and you get a curve. With the usual choices for axes, all curves should look like the blue one.
 

Thread 'Hypothesis testing: Defining H0, HA hypotheses so that ( H_A)_A' makes sense'

The standard _A " operator" maps a Null Hypothesis Ho into a decision set { Do not reject:=1 and reject :=0}. In this sense ( HA)_A , makes no sense. Since H0, HA aren't exhaustive, can we find an alternative operator, _A' , so that ( H_A)_A' makes sense? Isn't Pearson Neyman related to this? Hope I'm making sense. Edit: I was motivated by a superficial similarity of the idea with double transposition of matrices M, with ## (M^{T})^{T}=M##, and just wanted to see if it made sense to talk...
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