A statistical test for Nested Sampling algorithms

Understand

Nested sampling is an iterative integration procedure that shrinks the prior volume towards higher likelihoods by removing a "live" point at a time.

• A replacement point is drawn uniformly from the prior above an ever-increasing likelihood threshold.
• Thus, the problem of drawing from a space above a certain likelihood value arises naturally in nested sampling, making algorithms that solve this problem a key ingredient to the nested sampling framework.
• If the drawn points are distributed uniformly, the removal of a point shrinks the volume in a well-understood way, and the integration of nested sampling is unbiased.