A published fit of a resonance amplitude and its decay time reports and

PHYSICS · Subjective · Fermi University Physics · Scientific Practice & Experimental Methods · Data analysis and model fitting in the laboratory · Data analysis and model fitting in the laboratory

Computational Physics, Ch Finding the best parameters: minimisation and fitting

Problem

A published fit of a resonance amplitude AA and its decay time τ\tau reports A=(…)±2.0 mVA = (\ldots) \pm 2.0\,\mathrm{mV} and τ=(…)±0.05 ms\tau = (\ldots) \pm 0.05\,\mathrm{ms}, with a stated correlation ρ=−0.80\rho = -0.80 between them, but does not give the curvature matrix that produced these numbers. (a) Reconstruct the covariance matrix Cov\mathrm{Cov} from σA\sigma_A, στ\sigma_\tau and ρ\rho. (b) Reconstruct the curvature matrix H=2 Cov−1H = 2\,\mathrm{Cov}^{-1} that a finite-difference calculation of ∂2χ2/∂pj∂pk\partial^2\chi^2/\partial p_j\partial p_k at the minimum should reproduce.

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