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Add log_inc_beta function #2790
Description
Description
The Binomial (LC)CDF functions are defined using the inc_beta function, however this can underflow to 0 for large inputs. By using the relationship with the Gauss Hypergeometric function, we can calculate inc_beta on the log scale: https://stats.stackexchange.com/a/148700
This provides greater resistance to underflow: https://godbolt.org/z/Pxn8MMYTv
Current Version:
v4.4.0
Activity
spinkney commentedon Jul 14, 2022
Be careful with this as it does lose a lot of precision for very small
xvalues. See discussion at https://bugs.r-project.org/show_bug.cgi?id=16332#c7. We'll have to branch across different values ofx.spinkney commentedon Jul 14, 2022
Umm, when I tested this in R it wasn't good but boost's implementation in c++ is good in a wide range of
xvalues.andrjohns commentedon Jul 15, 2022
Hmm, well it's not the easy fix I was hoping for, but it's a start!
Once we've got the
2F1in I'll start investigating where the underflow could be coming fromandrjohns commentedon Jul 15, 2022
But I also only brought this up for the beta/binomial CDFs (numerical stability for copulas), so let me know if there's a better or more robust approach that avoids all of these headaches!
spinkney commentedon Jul 17, 2022
I think what you have will work! Looking forward to more stable cdfs!
avehtari commentedon Oct 8, 2026
#3433 improves stability, but below
DBL_MINlog_inc_betais still needed