Reliability Of Error Estimator Research Articles

Experimental estimation of uncertainties in powder diffraction intensities with a two-dimensional X-ray detector

A method to obtain both one-dimensional powder diffraction intensities I(2θ) and statistical uncertainties σ(2θ) from the data collected with a flat two-dimensional X-ray detector is proposed. The method has been applied to analysis of the diffraction data of fine quartz powder recorded with synchrotron X-ray. The profile and magnitude of the estimated uncertainties σ(2θ) have shown that the effects of propagation of the errors in 2θ are dominant as the uncertainties about the observed intensity values I(2θ). The powder diffraction intensity data I(2θ), including nine reflection peaks have been analyzed by the Rietveld method incorporating the experimentally estimated uncertainties σ(2θ). The observed I(2θ) data have been reproduced with a symmetric peak profile function (Rwp = 0.84 %), and no significant peak shifts from calculated locations have been detected as compared with the experimental errors. The optimized values of the lattice constants of the quartz sample have nominally been estimated at a = 4.9131(4) Å and c = 5.4043(2) Å, where the uncertainties in parentheses are evaluated by the Rietveld optimization based on the estimated uncertainties σ(2θ) for intensities I(2θ). It is likely that reliability of error estimation about unit-cell dimensions has been improved by this analytical method.

Reliability of error estimates from the minimal model: implications for measurements in physiological studies

MINMOD provides an estimate of the error in the insulin sensitivity index (SI) and glucose effectiveness at basal insulin (Sg) as the fractional standard deviation (FSD). The validity of the FSD estimate has not been assessed in a large number of human studies, nor has a comparison of the accuracies achievable using the two different intravenous glucose tolerance test (IVGTT) protocols (glucose only and tolbutamide protocol) been performed. To address these two issues, we obtained the FSD value and performed Monte Carlo simulations for 237 IVGTT studies. The FSD underestimated the true error as determined as the coefficient of variation from Monte Carlo simulation (COV-MC) with the ratio of COV-MC to FSD being 3.07 +/- 0.20 (mean +/- SE) for SI using the tolbutamide protocol. Additionally, the mean COV-MC for glucose-only protocol was approximately two to three times that for the tolbutamide protocol for both SI and Sg. We conclude that FSD underestimates the true error in SI and Sg. Additionally, more accurate results are obtained from the tolbutamide protocol than with the glucose-only protocol.