Normal_lcdf underflows much faster than pnorm(log=TRUE)

[Bob_Carpenter]

@mat_weldon

I now have doubts that the manual should suggest that it can be used instead of normal_lcdf for probit regression (P.448) without further checks. It might look ok on the original scale, but on the log scale it looks like a bad approximation.

Sorry that was misleading. Phi_approx is just a inverse logit scaled to look like probit.

@mat_weldon

without further checks

We encourage people to check every aspect of their fits! This stuff’s all way too numerically unstable to trust out of the box for complicated problems without validation. It also helps check the coding part in addition to the statistics.

@mat_weldon

This is the same point at which R’s pnorm underflows to 0, but pnorm with log=TRUE gives an answer (presumably accurate) until the argument is less than −1×10154-1 \times 10^{154}.

There’s a lot of room for improvement in our _lcdf and _lccdf functions—they’re mostly just taking the log of the _cdf functions.

We’d love to have someone work on this.

If there are specific algorithms people can recommend for the normal log CDF, we could implement those.