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

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.