Straight line regression through data with correlated uncertainties in two or more dimensions, with an application to kinetic isotope fractionation

摘要: Abstract Straight line regression algorithms are used frequently for measured data that contain non-negligible uncertainties in each variable. For the general case of correlated measurement between two variables differ from one analysis to next, popular algorithm York, 1968 calculates maximum likelihood estimate parameters and their uncertainties. However, it considers only two-dimensional omits uncertainty correlation slope y -intercept, an important term evaluating confidence intervals away origin. This contribution applies method straight through any number dimensions calculate a vector-valued intercept as well covariance matrix describes correlations. The is applied Pb by TIMS with silica gel activator define fractionation three dimensional log-ratio space. While log-ratios even mass isotopes follow predicted mass-dependent Rayleigh or exponential law within calculated uncertainties, containing odd isotope 207 diverges significantly, exhibiting mass-independent fractionation. appropriate lines form linear trends space, but not isochrons mixing lines, which be when plotted compositional ratios.