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Robust Method for Confidence Interval Estimation in Outlier-Prone Datasets: Application to Molecular and Biophysical Data

Victor V. Golovko

TL;DR

This work develops a robust framework for estimating central values and confidence intervals from small, noisy datasets with outliers by combining Steiner's Most Frequent Value (MFV) with a hybrid parametric bootstrap (HPB). MFV yields a distribution-insensitive center $M_n$ and scale $ abla_n$ by minimizing the KL divergence against a Cauchy substitute, enabling robust estimates without discarding data. The MFV-HPB method is demonstrated on nuclear data, showing MFV-centered results and asymmetric, reliable confidence intervals even in the presence of large uncertainties and non-Gaussian distributions; the approach is then applied to half-life estimates, underscoring stability to data selection. The framework offers broad applicability to biomolecular assays and biophysical measurements where data scarcity, variability, and outliers impede traditional methods, providing interpretable central estimates and robust CIs without strong distributional assumptions.

Abstract

Estimating confidence intervals in small or noisy datasets is a challenge in biomolecular research when data contain outliers or high variability. We introduce a robust method combining a hybrid bootstrap procedure with Steiner's most frequent value (MFV) approach to estimate confidence intervals without removing outliers or altering the dataset. The MFV identifies the most representative value while minimizing information loss, ideal for limited or non-Gaussian samples. To demonstrate robustness, we apply the MFV-hybrid parametric bootstrapping (MFV-HPB) framework to the fast-neutron activation cross-section of the 109Ag(n,2n)108mAg reaction, a nuclear physics dataset with large uncertainties and evaluation difficulties. Repeated resampling and uncertainty-based simulations yield a robust MFV of 709 mb with a 68.27% confidence interval of [691, 744] mb, illustrating the method's interpretability in complex scenarios. Although the example is from nuclear science, similar issues arise in enzymatic kinetics, molecular assays, and biomarker studies. The MFV-HPB framework offers a generalizable approach for extracting central estimates and confidence intervals in small or noisy datasets, with resilience to outliers, minimal distributional assumptions, and suitability for small samples-making it valuable in molecular medicine, bioengineering, and biophysics.

Robust Method for Confidence Interval Estimation in Outlier-Prone Datasets: Application to Molecular and Biophysical Data

TL;DR

This work develops a robust framework for estimating central values and confidence intervals from small, noisy datasets with outliers by combining Steiner's Most Frequent Value (MFV) with a hybrid parametric bootstrap (HPB). MFV yields a distribution-insensitive center and scale by minimizing the KL divergence against a Cauchy substitute, enabling robust estimates without discarding data. The MFV-HPB method is demonstrated on nuclear data, showing MFV-centered results and asymmetric, reliable confidence intervals even in the presence of large uncertainties and non-Gaussian distributions; the approach is then applied to half-life estimates, underscoring stability to data selection. The framework offers broad applicability to biomolecular assays and biophysical measurements where data scarcity, variability, and outliers impede traditional methods, providing interpretable central estimates and robust CIs without strong distributional assumptions.

Abstract

Estimating confidence intervals in small or noisy datasets is a challenge in biomolecular research when data contain outliers or high variability. We introduce a robust method combining a hybrid bootstrap procedure with Steiner's most frequent value (MFV) approach to estimate confidence intervals without removing outliers or altering the dataset. The MFV identifies the most representative value while minimizing information loss, ideal for limited or non-Gaussian samples. To demonstrate robustness, we apply the MFV-hybrid parametric bootstrapping (MFV-HPB) framework to the fast-neutron activation cross-section of the 109Ag(n,2n)108mAg reaction, a nuclear physics dataset with large uncertainties and evaluation difficulties. Repeated resampling and uncertainty-based simulations yield a robust MFV of 709 mb with a 68.27% confidence interval of [691, 744] mb, illustrating the method's interpretability in complex scenarios. Although the example is from nuclear science, similar issues arise in enzymatic kinetics, molecular assays, and biomarker studies. The MFV-HPB framework offers a generalizable approach for extracting central estimates and confidence intervals in small or noisy datasets, with resilience to outliers, minimal distributional assumptions, and suitability for small samples-making it valuable in molecular medicine, bioengineering, and biophysics.
Paper Structure (7 sections, 22 equations, 6 figures, 3 tables)

This paper contains 7 sections, 22 equations, 6 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. The most frequent value
  4. Bootstrapping for Robust Confidence Interval Estimation
  5. Description of the Methods and Results
  6. Discussion
  7. Conclusion

Figures (6)

  • Figure S1: A histogram of fast-neutron (14.7$\pm$0.2 MeV) activation cross-sections (see Table \ref{['tab:sigma_table']}) of the $^{109}\text{Ag}(\text{n},2\text{n})^{108m}\text{Ag}$, showcasing the weighted average (399 mb), arithmetic mean (638 mb), and MFV (685 mb) as measures of central tendency. In addition, the smooth red curve shows the Gaussian fit of the data.
  • Figure S2: A histogram of fast-neutron (14.7$\pm$0.2 MeV) activation cross-sections (re-evaluated) for the $^{109}\text{Ag}(\text{n},2\text{n})^{108m}\text{Ag}$ reaction displays the weighted average (728 mb), arithmetic mean (718 mb), and MFV (709 mb) as indicators of central tendency. The smooth red curve shows a Gaussian fit to the data.
  • Figure S3: Histograms of randomized bootstrap sample values for four selected cross-section measurements ($x_1$, $x_2$, $x_3$, $x_4$). Each histogram is fitted with a Gaussian function, and the original values with uncertainties from Table \ref{['tab:sigma_table']} are marked with vertical black lines. Fit results and absolute percent differences are indicated.
  • Figure S4: A histogram of the MFV for fast-neutron (14.7$\pm$0.2 MeV) activation cross-sections for the $^{109}\text{Ag}(\text{n},2\text{n})^{108m}\text{Ag}$ reaction for data from Table \ref{['tab:sigma_table']} (original). Hybrid parametric bootstrapping for 68.3% confidence interval and the MFV are also shown.
  • Figure S5: A histogram of the MFV for fast-neutron (14.7$\pm$0.2 MeV) activation cross-sections for the $^{109}\text{Ag}(\text{n},2\text{n})^{108m}\text{Ag}$ reaction for data from Table \ref{['tab:Ag108m_14_7MeV']} (re-evaluated). Hybrid parametric bootstrapping for 68.27% confidence interval and the MFV are also shown.
  • ...and 1 more figures