A new arXival on nested sampling, Snowballing Nested Sampling by Johannes Buchner, just appeared. The idea behind this short note is to increase the number of “live” points at each iteration. (How?! Depending on how the different additions are dependent, the effective sample size will vary.) This exacerbates the tendency of the algorithm to concentrate on high density regions.
“Loosely speaking, each dead point from a run with K is split into two dead points from a run with K′ live points. The noise in the nested sampling estimate due to more dead points is also reduced, because the variance is inversely proportional to K.”
The following line is most puzzling (K being the number of live points and M the number of MCMC steps to simulate from the restricted prior):
“Based on this [argument], K → ∞ with fixed M achieves the properties of M → ∞ with fixed K.”
which connects with the ambiguity of running the MCMC move at each nested iteration a certain number M of steps, even though I always thought a single step was theoretically enough. In practice, this single step may further take forever if no trick is available for simulating from the constrained prior. And when K increases, so does the correlation unless iid sampling can be implemented, which does not sound realistic.
