A definition is given at the beginning of secion 5.3.
The performance of the tau identification algorithm in terms of the
inverse background efficiency, 1/εbkg versus the signal identification efficiency, εsig is shown in Fig. 9.
The identification efficiency is defined as the fraction of 1-prong (3-prong) hadronic tau decays that are reconstructed as 1-track (3-track) τhad−vis candidates, which also pass the BDT selection criteria. The
efficiency is the product of the reconstruction efficiency defined in section 4.3 and of the identification
efficiency.
I'm not an expert in this field. But it reads to me like the background efficiency is akin to a false positive probability, and the signal efficiency is akin to a true positive probability. So Fig. 9 is a kind of ROC curve, but with the inverse false positive probability instead of the false positive probability.
I don't see any particular reason why you couldn't reproduce the Foucault experiment with bronze age technology. Foucault measured the speed of light to better than 1% - not quite the 0.1% requested, but very close. If you give Ptolemy Foucault's procedure, he can probably duplicate it, although he won't know what a meter is.
One second is 1/86400 of the time between consecutive sunrises (or, for greater accuracy, between consecutive cycles of the celestial sphere, or between consecutive sunrises at the winter or summer solstice). Ptolemy can tune a pendulum and count. No atomic clocks required, the planet is a perfectly good clock at the desired precision.
Given the second and the speed of light, we have the definition of the meter and Ptolemy can convert to meters if he suddenly gets the perverse desire to define a unit of length that no-one else uses, equal to exactly 1/299792458 the distance light travels in a second.
Ptolemy can blow glass into a pipette, put some mercury in it, and graduate it 100 times between the freezing point and boiling point of water, so he has the same temperature units that we have.
Ptolemy can make another graduated pipette, this time with water in it, gradually heat the water to discover that its maximal density is found at 4 marks above freezing on his mercury pipette, and use volumes of water at maximal density for mass. One liter of water at 4 degrees is 1 kilogram to much better than 0.1%, so now Ptolemy has a unit (based on cubic light-days, which are convertible into liters filled with maximally dense water) which is convertible into kilograms.
Ptolemy now has meters, seconds, and kilograms, so he has newtons, joules, and so on.
We can give Ptolemy a measurement for volts (in terms of centimeters of dielectric breakdown of dry air) by having him experiment with triboelectricity, which should have a precision of about +/- 1%. Not great, but pretty good. Given units convertible to volts, joules, meters, and seconds, Ptolemy now has ohms, amperes, coulombs, and so on. He's good to go unless we need him to start writing about quarks.
Best Answer
This answer is framed in terms of particle physics, but the basic idea can be generalized to any analysis where the presence or absence of the thing you are trying to study must be deduced from the raw data.
Many particle physics detectors collect data in a very general sense, and to study something in particular you need to select from all the myriad recorded events that those that correspond to the physics you want to study.
That is, you are going to partition the whole data set into those events that you believe represent your physics and those that do not. Obviously you can make two classes of errors in that partition:1
The term signal efficiency is usually defined as the fraction of the desired events that you actually get (i.e. it goes down as the false negative rate goes up). The term background rejection is usually defined as the fraction of events that don't belong in your sample that are excluded from your sample (i.e. it goes down as the false positive rate goes up).
1 And it is generally the case that the harder you work to prevent one class of errors the more of the other class you are going to get, so there is a trade-off here.