binningverdict: A unified decision system for logarithmic versus linear binning of small-angle neutron scattering data
Description
We present binningverdict, an open-source Python package for quantitatively selecting logarithmic or linear binning in small-angle neutron scattering (SANS) data reduction. The framework combines correlation-aware variance–bias optimization with Fisher-information analysis in a computationally efficient workflow operating directly on measured (Q, I, σ) profiles. Central to the method is a closed-form reconstruction-error ratio, 𝑅_{MSE}=𝐸*_{log}/𝐸*_𝐿, obtained by extending the Freedman–Diaconis mean-squared-error decomposition to Q-dependent bin widths. The resulting expression depends only on four elementary moments of the data and is entirely model-free. An optional Fisher-information module evaluates finite-N parameter-estimation precision and demonstrates asymptotic scheme-independence between logarithmic and linear discretizations. The package provides convergence diagnostics, batch-processing capability, and millisecond-scale execution using only NumPy. Benchmarks on canonical SANS models, together with applications to measured EQ-SANS datasets, demonstrate robust performance and establish the framework as a practical tool for automated SANS reduction and preprocessing workflows.