Optimum strategies for inverse problems in statistical astronomy.
Abstract
Maximum penalized likelihood is investigated as an estimation procedure for the class of inverse problems that relate an unobservable to an observable probability density function (pdf). For a simple test problem, results derived with different penalizing techniques are quantitatively compared by computing the KolmogorovSmirnov distances (D_KS_) between the estimated and the exact pdfs. Optimum estimates (minimum D_KS_) derived by iterative inversion are found to be superior to those derived with an entropic penalty function using a uniform default solution. However, if entropy is defined relative to an adaptive default solution, the optimum maximum entropy (ME) estimates can become comparable in precision to optimallystopped iterative inversions. In addition, a stopping criterion is found that closely locates the optimum iteration at which to stop iterative inversions. No comparable criterion is identified for locating the optimum regularization constant for ME estimation, but a simple feasibility criterion on the probability of the data results in only modest loss of precision relative to the optimum.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 September 1994
 Bibcode:
 1994A&A...289..983L
 Keywords:

 Algorithms;
 Astronomy;
 Maximum Likelihood Estimates;
 Optimization;
 Problem Solving;
 Statistical Tests;
 Strategy;
 Iterative Solution;
 KolmogorovSmirnov Test;
 Maximum Entropy Method;
 Probability Density Functions;
 Probability Distribution Functions;
 Astronomy;
 METHODS: DATA ANALYSIS;
 METHODS: STATISTICAL;
 TECHNIQUES: IMAGE PROCESSING