and another one on nested sampling

The same authors as those of the paper discussed last week arXived a paper on dynamic nested sampling.

“We propose modifying the nested sampling algorithm by dynamically varying the number of “live points” in order to maximise the accuracy of a calculation for some number of posterior sample.”

Some of the material is actually quite similar to the previous paper (to the point I had to check they were not the same paper). The authors rightly point out that the main source of variation in the nested sampling approximation is due to the Monte Carlo variability in the estimated volume of the level sets.

The main notion in that paper is that it is acceptable to have a varying number of “live” points in nested sampling provided the weights are correctly accordingly. Adding more of those points as a new “thread” in a region where the likelihood changes rapidly. Addition may occur at any level of the likelihood, in fact, and is determined  in the paper by an importance weight being in the upper tail of the importance weights… While the description is rather vague [for instance I do not get the notation in (9)] and the criteria for adding threads somewhat arbitrary, I find interesting that several passes at different precision levels can improve the efficiency of the nested approximation at a given simulation cost. Remains the issue of whether or not this is a sufficient perk for attracting users of other simulation techniques to the nested galaxy…