Nested Sampling was developed by John Skilling (http://www.inference.phy.cam.ac.uk/bayesys/box/nested.pdf // http://ba.stat.cmu.edu/journal/2006/vol01/issue04/skilling.pdf).
The basic idea is that in order to reach to the ultimate region of interest one needs to contract the search space into itself. Assuming no loss in generality and assuming the risk of contracting the region of interest, one proceeds to nest the sampling space. The guiding philosophy is that "nature abhors gradient".
What is nice about this algorithm is the fact that we get Posterior distribution and the evidence as the by product of each other.
The evidence indicates the strength of the model and the posterior depicts the learning pattern.
(to be continued)