High-fidelity covariance estimation in Feynman- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si113.svg" display="inline" id="d1e1312"> <mml:mi>α</mml:mi> </mml:math> analysis using raw-data bootstrapping and a hybrid fitting frame

In Feynman- α analysis, it is common practice to employ the bunching technique on the measured neutron counting events. This method synthesizes neutron count data with larger bin widths by aggregating counts from smaller bin widths. For each resulting bin size T , the variance-to-mean ratio Y ( T ) is computed. The resulting Y-curve forms the basis for determining the α parameter by fitting the data. However, this process inherently introduces strong correlations among the data points of the Y-curve, making the accurate estimation of the full covariance matrix a critical prerequisite for a robust uncertainty quantification of the α value. This work addresses the challenge of determining the covariance matrix by applying the bootstrap method directly on the raw, unbinned time-series data—specifically, the time differences between consecutive detector events. From a single experimental time series, the bootstrap method generates a large ensemble of resampled data sets. The bunching technique is subsequently applied to each resampled set to construct a corresponding ensemble of Y-curves. We demonstrate that the covariance matrix derived from this ensemble constitutes a high-fidelity estimate of the full, true covariance matrix, showing excellent agreement with reference matrices derived from extensive first-principle simulations. Despite its accuracy, the direct application of this bootstrap-derived covariance matrix in a least-squares fit is computationally prohibitive for routine analysis where the α value and its uncertainty are required shortly after the Feynman- α measurement, particularly for guiding ongoing experimental campaigns. To overcome this limitation, we present a novel hybrid methodology. This approach synergistically combines the accuracy of the raw-data bootstrapping with the computational efficiency of the batch-based fitting algorithm presented in our previous work. This hybrid method is shown to yield parameter estimates and uncertainties that are statistically consistent with the high-fidelity approach, while drastically reducing the computational effort. This work thus provides a new, powerful framework that resolves the trade-off between statistical accuracy and computational feasibility in Feynman- α analysis. • Raw-data bootstrapping on timestamps adapted for Feynman- α covariance estimation. • Accuracy validated using a synthetic generator and 30,720 reference simulations. • A hybrid framework combines raw-data bootstrapping with snippet batching. • Hybrid method cuts bootstrap resamples by ∼ 10 × while keeping consistency.