Principle of the NS algorithm (taken from Skilling & MacKay 2012): the upper part of both panels describes a contour plot of a likelihood function ℒ(θ). Left panel: a) each point θ within parameter space ℘ defined by the parameter ranges of θ₁ and θ₂ is associated with the volume that would be enclosed by the contour L = ℒ(θ). (L(x) is the contour value such that the volume enclosed is x.) If the points θ are uniformly distributed under the prior probability distribution (prior), all these volumes (x-values) are uniformly distributed between 0 and 1. Right panel: b) using a Markov chain method, the NS algorithm takes a point (purple dot) from ℘ satisfying L ≥ L(x₁). Inserting the new point into this distribution, we can find the highest x-value x₂ used for the next iteration.