clarify "acceptance-walk" in dynesty guide
Dear maintainers, this is a partial attempt to make the dynesty guide's description of the "acceptance-walk" method easier to understand. The current version is
with this method, the length of each MCMC chain is predetermined. The specific length evolves during the run to yield an average of naccept accepted jumps during each chain. This method is well suited to parallelised applications, as each MCMC chain will run for the same amount of time. The value of naccept should be tuned based on the application. For example, one could run a single analysis with sample="act-walk" to estimate a viable number of accepted steps.
where, to me at least, the first two sentences seem directly contradictory - if it's "predetermined", how can it "evolve"? I only understood what was meant when checking the internal page https://git.ligo.org/lscsoft/bilby_pipe/-/wikis/O4-review/dynesty-updates : to my best understanding now, the "predetermined" was meant to refer to within a single iteration of the overall nested sampling loop. What do people think, does my edit catch that better? I'd also be happy for this MR to be discarded and for a true expert to make a different clarification.
Other aspects that could be good to address at the same time:
- What exactly does the "average" refer to, just for the lifetime of a single-point single-iteration updating step, across all chains that are run in all updates of a specified live point, or the whole run?
- Should the volumetric->differential proposal change (mentioned on the wiki) also be mentioned here in the docs?