xsample() : An R Function for Sampling Linear Inverse Problems

Abstract

Underdetermined linear inverse problems are often solved by minimizing or maximizing a chosen solution norm. When there are no strong arguments for selecting a solution norm, as is often the case in ecological models, it is interesting to sample the whole solution space.We propose a new method for sampling the solution space of an underdetermined linear inverse problem. A Markov Chain Monte Carlo algorithm produces a sample set that represents the probability distribution of all solutions. By ensuring an acceptance rate of 100%, the number of iterations is limited to a minimum which speeds up the calculation time significantly, even for problems with a large number of unknowns.