An iterative technique for the rectification of observed distributions

TLDR

The authors propose an iterative technique for estimating solutions to rectification and deconvolution problems in statistical astronomy, and suggest its use for generating unbiased, smoothed histograms. The method, based on Bayes’ theorem, preserves distribution constraints and iteratively increases likelihood, and is applied to rectify v sin i distributions for aspect effects and to correct radio‑astronomical observations for beam‑smoothing. When tested on problems with known infinite‑sample solutions, the technique achieves excellent results after only a few iterations, and demonstrates similar performance in rectifying v sin i distributions and correcting beam‑smoothing effects.

Abstract

An iterative technique is described for generating estimates to the solutions of rectification and deconvolution problems in statistical astronomy. The technique, which derives from Bayes' theorem on conditional probabili- ties, conserves the constraints on frequency distributions (i.e., normalization and non-negativeness) and, at each iteration, increases the likelihood of the observed sample. The behavior of the technique is explored by applying it to roblems whose solutions are known in the limit of infinite sample size, and excellent results are obtained after a few iterations. The astronomical use of the technique is illustrated by applying it to the problem of rectifying distributions of v sin i for aspect effect; calculations are also reported illustrating the technique's possible use for correcting radio-astronomical observations for beam-smoothing. Application to the problem of obtaining unbiased, smoothed histograms is also suggested.