lccdf of beta overflows at reasonably normal values

[aakhmetz]

Dear all,

I am sorry for giving reference to Claude AI in advance, but it was flagged by it recently.

transformed data { real y = 0.865169; }
generated quantities {
  real lccdf = beta_lccdf(y | 1, 19);   //   -inf
  real truth = 19 * log1m(y);           //  -38.0709
}

Analytically that's beta_lccdf(y | 1, 19) = 19·log1m(x) = −38.07, entirely finite. Stan evaluates it as log(1 − inc_beta(...)), and (1−0.865)^19 = 3e-17 vanishes against 1.0 in double precision, so it returns log(0), which leads to initialization error.

Technically, I have also had similar problems working with log_diff_exp for _lcdf. So I replaced it with log(CDF1 - CDF2) and it worked quite fine.

Sorry if I disturbed you without a good reason in advance.

Best wishes,
Andrei

[SteveBronder]

Thanks for this! This has come up in a few cdf functions and I think we need to do a bigger review of extreme values for all of them. This would be a nice thing for a swarm of claude agents to look at since it would just be researching extreme values for each distribution and putting those into our expect_ad testing framework.