sentences:  The nested sampling algorithm was developed by John Skilling specifically to approximate these marginalization integrals, and it has the added benefit of generating samples from the posterior distribution formula_18.It is an alternative to methods from the Bayesian literature such as bridge sampling and defensive importance sampling.Here is a simple version of the nested sampling algorithm, followed by a description of how it computes the marginal probability density formula_19 where formula_20 is formula_1 or formula_2