Statistics is used everything and is something you don't want to miss. Here's just some of my understanding.



What is Statistical Error?

What is Systematic Error?

Auxiliary measurements provide uncertainties for measured variables. Those variables are used in analysis. Explicitly variables are like luminosity, calibration factor and scale factor inside a certain object bin of pt vs eta; implicitly, they can be "the effect of changing your smearing algorithm", "changing your underlying parton distribution function", etc. They are given by auxiliary measurement in a 1 sigma deviation manner.

The 1 sigma variation will be usually assigned to a gaussian constraint, Gaus( θ ; mean = 0, sigma = 1), and prediction will be sth like (nominal * (1 + variation * θ)). This is based on the assumption that 1 sigma variation on your parameter will have a 1 sigma variation impact on the final result.

See here for some introduction to systematic uncertainty. It also introduce something about profile likelihood, which absorb the nuisance parameters
[ Pekka K. Definition and Treatement of Systematic Uncertainties in High Energy Physics and Astrophysics].

What is a fit?

A fit is a procedure to find minimum/maximum of a certain metric.

Best Fit Interpretation


Errors are usually calculated assuming 1 sigma deviation from nominal, by convention. So nuisance parameter are usually assigned to a Gaussian constraint with sigma=1. If the estimated error given by fitting algorithms is less than 1, we have underconstrain. If it's over 1, we have overconstrain.

The estimated errors given by the the fitting algorithm are what the algorithm defines 1sigma error. So if you have underconstrain, for example 0.9, the algorithm thought your error should be 0.9 * variation_1sigma, so you have overestimated your error

Technical procedure of fitting

Fitting algorithms

Algorithm of errors

Examples of metrics

Some tutorials

-- RongkunWang - 2017-09-04

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