Solutions of the bivariate, linear errors-in-variables estimation problem with unspecified errors are expected to be invariant under interchange and scaling of the coordinates. The appealing model of normally distributed true values and errors is uni
dentified without additional information. I propose a prior density that incorporates the fact that the slope and variance parameters together determine the covariance matrix of the unobserved true values but is otherwise diffuse. The marginal posterior density of the slope is invariant to interchange and scaling of the coordinates and depends on the data only through the sample correlation coefficient and ratio of standard deviations. It covers the interval between the two ordinary least squares estimates but diminishes rapidly outside of it. I introduce the R package leiv for computing the posterior density, and I apply it to examples in astronomy and method comparison.
We compare and contrast three different perturbative expansions for the quartic anharmonic oscillator wavefunction and apply a modified Borel summation technique to determine the energy eigenvalues. In the first two expansions this provides the energ
y eigenvalues directly however in the third method we tune the wavefunctions to achieve the correct large x behaviour. This tuning technique allows us to determine the energy eigenvalues up to an arbitrary level of accuracy with remarkable efficiency. We give numerical evidence to explain this behaviour. We also refine the modified Borel summation technique to improve its accuracy. The main sources of error are investigated with reasonable error corrections calculated.
