Encounters
Autocorrelation ○｜encounter｜ENC｜20260715134600-00-•
Hey Cal,
For degeneracy, the corner plot is the first step to clearly depict the (modeling - not physical) correlations. The first step is simply to present them cleanly; with the MCMC (assuming it is converged) you actually have cleanly mapped the confidence interval of the joint posterior. For a parameter that should be invariant - like NH - our approach was to fix it at a reference value, which then nixes its degeneracy with the spin. But we will still explore that by scoping out a range of plausible NH values. However, while a* should be invariant, its the parameter of interest so I wouldn’t want to go that route, because we want our investigation to be a thorough examination of its value and uncertainty. And f_sc is a dynamic quantity so it. makes life messy! That’s the nature of the beast. Depending on what the autocorrelation reveals, it might be reasonable to have you overlay a set of posteriors (e.g., different colors each) in f_sc, a* space for selectable spectra. If the distributions are are all within bounds, but the tails to low spin go with high fsc (maybe with poorer S/N) then we could try to do something more robust. If they are truly distributed outside the error bounds, then that points to hidden systematics of the model. In any case this is getting longwinded - the tl;dr is if the MCMC isn’t overly expensive to run to convergence then we should do that at the nominal M i D for the full selectable set. Convergence, by the way, would be something like if each walker has exceeded its autocorrelation length by >~20x, ideally ~100x.
-Jack
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