Overview¶
PyUnfold is a Python package for incorporating imperfections of the measurement process into a data analysis pipeline.
What is unfolding?¶
In an ideal world, we would have access to the perfect detector: an apparatus that makes no error in measuring a desired quantity. However, in real life, detectors have:
- Finite resolutions
- Characteristic biases that cannot be eliminated
- Less than 100% detection efficiencies
- Statistical uncertainties
By building a matrix that encodes a detector’s smearing of the desired true quantity into the measured observable(s), a deconvolution can be performed that provides an estimate of the true variable. This deconvolution process is known as unfolding.
Iterative unfolding¶
The unfolding method implemented in PyUnfold accomplishes this deconvolution by harnessing the power of Bayes’ Theorem in an iterative procedure, providing results based on physical expectations of the desired quantity [1]. Furthermore, tedious book-keeping for both statistical and systematic errors produces precise final uncertainty estimates.
Terminology¶
In the measurement process, a true distribution of causes is detected by some apparatus having a characteristic response function, or matrix, which produces a measurable distribution of effects.
The act of unfolding approximates the inverse of the response function by convolving it with a prior distribution which encodes a guess at the form of the true cause distribution. Including the measured effects distribution, we obtain an improved estimate of the cause distribution. This updated, better guess can be used as a prior for another unfolding, making this an iterative procedure.
These unfolding iterations continue until some stopping condition (a test statistic comparing the unfolded cause distribution between subsequent iterations) satisfies some pre-defined threshold, typically taking just a few iterations.
To use PyUnfold, one needs only to provide the
- Measured effects distribution
- Response matrix
- Prior distribution
For further mathematical details on the unfolding procedure, see the Mathematical Derivations section.
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