A snippet-based algorithm for practical covariance estimation in Feynman-α analysis

Abstract

In the context of Feynman-$\alpha$ analysis, the bunching technique is a widely used method for synthesizing neutron count data with larger bin widths by aggregating counts from smaller bin widths. For each bin size $T$, the variance-to-mean ratio $Y\left(T\right)$ is computed, forming the basis for determining the $\alpha$ parameter. However, the points on the $Y\left(T\right)$ curve are inherently correlated due to the bunching process. As a result, uncorrelated fitting methods that rely solely on the standard errors of $Y\left(T\right)$ fail to provide accurate estimates for $\alpha$ and its uncertainties. A proper treatment of these correlations requires incorporating the covariance matrix of the $Y\left(T\right)$ points into the fitting procedure. In practice, estimating this covariance matrix from real measurements is challenging and demands a large amount of data, while its theoretical estimation remains an open problem. This paper investigates alternative approaches to reliably determine $\alpha$ and its uncertainties. Our analysis confirms that uncorrelated fits, neglecting the covariance matrix, fail to provide reliable uncertainties as correlations are significant. Conversely, including an accurately estimated covariance matrix yields correct results for $\alpha$ and its uncertainties. Since direct estimation of the full covariance matrix requires extensive data, entailing significant measurement time and computational effort, a new method is proposed. This method enables the estimation of the necessary covariance information within practical limits of measurement time and computational resources. These findings reinforce the theoretical foundation of Feynman-$\alpha$ analysis and offer a robust framework for accurately fitting correlated data arising from the bunching technique.