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add ultranest import #313
add ultranest import #313
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If I understand correctly, the only thing we need from this is the paramnames entry, although it is nice that it has a maximum likelihood point. Presuming this is found by an optimisation procedure (like e.g. polychord's polishing
settings.maximise=true
gives) then this is could be useful in future iterations.There was a problem hiding this comment.
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This is the last live point discarded, but for the default frac_remain=0.01 this is good enough.
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Theoretically I disagree -- the rule of thumb is that
logLmax ~ <logL>_P + d/2
, and the width of the typical set inlogL
space issqrt(d/2)
, so in even moderate dimensions the true likelihood peak lies some distance away from where nested sampling terminates, regardless of stopping criterion (see figure 2), but this isn't relevant to this PR!There was a problem hiding this comment.
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I have been wondering if we could somehow make use of PolyChord's
maximise=true
output in anesthetic...There was a problem hiding this comment.
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I think in practice all of these would work fine for a run that had reached convergence. I would worry if you also started trying to use it at different temperatures.
As an API, a better solution would be for the maximum to be appended with a logL_birth=logL=logL_max, so it's officially 'beyond the last live point'.
We'd then have to write the volume calculation to ensure anesthetic set these to zero or nan weight by default, since there's no way to determine the volume if there's a gap.
I could imagine gaps occurring naturally in the case of importance weighting.
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Issue raised in #317.
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As an aside, I have been working through this analytically and experimentally this afternoon, and this statement only holds in higher dimensions.
Here is an analytic result for f=0.01, n=1000 for how close you get in loglikelihood to the maximum as a function of dimension: