Proceedings Article | 22 September 1998

Proc. SPIE. 3459, Bayesian Inference for Inverse Problems

KEYWORDS: Statistical analysis, Optical spheres, Error analysis, Computer programming, Computer simulations, Tomography, Monte Carlo methods, Distance measurement, Reconstruction algorithms, Computer programming languages

In many real-life situations, it is very difficult or even impossible to directly measure the quantity y in which we are interested: e.g., we cannot directly measure a distance to a distant galaxy or the amount of oil in a given well. Since we cannot measure such quantities directly, we can measure them indirectly: by first measuring some relating quantities x<SUB>1</SUB>,...,x<SUB>n</SUB>, and then by using the known relation between x<SUB>i</SUB> and y to reconstruct the value of the desired quantity y. In practice, it is often very important to estimate the error of the resulting indirect measurement. In this paper, we show that in a natural statistical setting, the problem of estimating the error of indirect measurement can be formulated as a simplified version of a tomography problem. In this paper, we use the ideas of invariance to find the optimal algorithm for solving this simplified tomography problem, and thus, for solving the statistical problem or error estimation for indirect measurements.