Opening up Nested Sampling

Abstract

We open up nested sampling (NS) to new applications by viewing NS as a general algorithm for tackling compression. We demonstrate this through two non-traditional applications of NS to problems in likelihood-free and frequentist computation that suffer from compression. We then discuss advances in diagnostics for NS runs. We describe how we can test sampling from the constrained prior by opening up individual NS runs and analyzing the insertion indexes of new live points. Lastly, we open up the heuristic formula for NS errors based on information, and show that when the sums are carefully expanded it matches an expression based on an analysis of the moments of the compression factors.