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An Iterative, Dynamically Stabilized(IDS) Method of Data Unfolding

Bogdan Malaescu

TL;DR

The paper addresses distortions in experimental spectra caused by detector effects and background subtraction, introducing a dynamically regularized iterative unfolding (IDS) method. It combines a monotone regularization function, a robust data/MC normalization that accounts for new structures, and iterative refinement of the folding/unfolding matrices to recover true spectra even when new features are present. Key contributions include a fluctuation-aware normalization, adaptive unfolding through a three-step iteration, and an effective update of the transfer matrix guided by data. The method is demonstrated on complex, realistic examples, showing robust recovery of structures and controlled propagation of background fluctuations, with practical implications for high-energy physics data analysis.

Abstract

We describe an iterative unfolding method for experimental data, making use of a regularization function. The use of this function allows one to build an improved normalization procedure for Monte Carlo spectra, unbiased by the presence of possible new structures in data. We unfold, in a dynamically stable way, data spectra which can be strongly affected by fluctuations in the background subtraction and simultaneously reconstruct structures which were not initially simulated.

An Iterative, Dynamically Stabilized(IDS) Method of Data Unfolding

TL;DR

The paper addresses distortions in experimental spectra caused by detector effects and background subtraction, introducing a dynamically regularized iterative unfolding (IDS) method. It combines a monotone regularization function, a robust data/MC normalization that accounts for new structures, and iterative refinement of the folding/unfolding matrices to recover true spectra even when new features are present. Key contributions include a fluctuation-aware normalization, adaptive unfolding through a three-step iteration, and an effective update of the transfer matrix guided by data. The method is demonstrated on complex, realistic examples, showing robust recovery of structures and controlled propagation of background fluctuations, with practical implications for high-energy physics data analysis.

Abstract

We describe an iterative unfolding method for experimental data, making use of a regularization function. The use of this function allows one to build an improved normalization procedure for Monte Carlo spectra, unbiased by the presence of possible new structures in data. We unfold, in a dynamically stable way, data spectra which can be strongly affected by fluctuations in the background subtraction and simultaneously reconstruct structures which were not initially simulated.

Paper Structure

This paper contains 10 sections, 2 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Important ingredients of the unfolding procedure
  3. The regularization function
  4. The MC normalization in presence of new structures in data
  5. The estimation of remaining fluctuations from background subtraction
  6. Folding and unfolding
  7. The improvement of the unfolding probability matrix
  8. The iterative unfolding strategy
  9. A complex example for the use of the unfolding procedure
  10. Conclusions

Figures (2)

  • Figure 1: Behaviour of the functions $f_{1..8}$ with respect to ${\Delta x}/{(\lambda \sigma )}$.
  • Figure 2: The unfolding result after 65 iterations (u, triangles), compared to the data distribution (d, filled circles), the reconstructed MC in the model ($\bar{\rm r}$,solid line) and the true MC model plus the new structures ($\bar{\rm t}+{\rm bias}$, dashed line).