Improved Maximum Entropy Analysis with an Extended Search Space
Abstract
The standard implementation of the Maximum Entropy Method (MEM) follows Bryan and deploys a Singular Value Decomposition (SVD) to limit the dimensionality of the underlying solution space apriori. Here we present arguments based on the shape of the SVD basis functions and numerical evidence from a mock data analysis, which show that the correct Bayesian solution is not in general recovered with this approach. As a remedy we propose to extend the search basis systematically, which will eventually recover the full solution space and the correct solution. In order to adequately approach problems where an exponentially damped kernel is used, we provide an opensource implementation, using the C/C++ language that utilizes high precision arithmetic adjustable at runtime. The LBFGS algorithm is included in the code in order to attack problems without the need to resort to a particular search space restriction.
 Publication:

arXiv eprints
 Pub Date:
 October 2011
 arXiv:
 arXiv:1110.6285
 Bibcode:
 2011arXiv1110.6285R
 Keywords:

 Physics  Computational Physics;
 High Energy Physics  Lattice;
 Nuclear Theory;
 Physics  Data Analysis;
 Statistics and Probability
 EPrint:
 18 pages, 6 figures, v3 includes several changes in text and figures, t.b.p. in Journal of Computational Physics, source code at http://www.scicode.org/ExtMEM