(7 6 22) Number of Lipka Bootstraps - JacobPilawa/TriaxSchwarzschild_wiki_5 GitHub Wiki

In Lipka and Thomas 2022, it's noticed that very few bootstraps are needed to optimize regularization. As Jacob and I discussed yesterday, it turns out that the same is true for all (continuous) parameters, such as Mbh, M/L, etc. The key is that the gradient of chi2posterior has much less scatter than the value itself. Thus, if we fit a GPR to a single bootstrap realization, we get a very reasonable estimate of meff from a single bootstrap. If we have multiple bootstraps, the key is to fit a GPR to each bootstrap individually and then average these bootstraps, rather than averaging over the bootstraps before fitting a GPR. Using this procedure, I find reasonable results after a single bootstrap, and results have almost entirely converged after 3 bootstraps. Here's are vertical plots comparing the parameter constraints (using chi2+meff) for different numbers of bootstraps. 0 bootstraps corresponds to chi2 without any meff term. The order in which bootstraps are added will obviously affect the convergence rate, so 3-5 bootstraps is probably ideal to be safe.

ST2	ST3
[ images/20220706/MQ/abel_st2_nboot.png ]] ](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[-images/20220706/MQ/abel_st3_nboot.png-)