A sampling strategy for high-dimensional spaces applied to free-form gravitational lensing

ABSTRACT We presentanovelproposalstrategyforthe Metropolis-Hastingsalgorithmdesignedtoefficiently sample general convex polytopes in 100 or more dimensions. This improvesupon previous sampling strategies used for free-form reconstruction of gravitationallenses, but is general enough to be applied to other fields. We have written a parallelimplementation within the lens modeling framework GLASS. Testing shows that weare able to produce uniform uncorrelated random samples which are necessary forexploring the degeneracies inherent in lens reconstruction.Keywords: gravitational lensing: strong - methods: numerical - methods: statistical 1 INTRODUCTIONSome inversion problems in astrophysics make it desirable tosearch or sample a high dimensional solution domain S⊂ R n such that Sis bounded by the linear constraintsAx6b (1)where A ∈ R m×n and bis a constant vector. A classic ap-plication is Schwarzschild’s construction of triaxial stellarsystems in equilibrium (Schwarzschild 1979). Given a three-dimensional discretized target density function ρ