I believe this is a docs issue with the normal distribution. The documentation at
https://mc-stan.org/docs/2_26/functions-reference/normal-distribution.html#normal-distribution says that Phi_approx is more robust in the tails. However, inspecting this shows that using normal_lcdf is actually more robust than Phi_approx.
Description:
Describe the issue as clearly as possible.
generated quantities {
vector[3] x;
vector[3] y;
real w;
real z;
real a;
x[1] = normal_lcdf(8 | 0, 1);
x[2] = normal_lcdf(9 | 0, 1);
x[3] = normal_lcdf(10 | 0, 1);
y[1] = log(Phi_approx(8));
y[2] = log(Phi_approx(9));
y[3] = log(Phi_approx(10));
w = log_diff_exp(y[3], y[2]);
z = log_diff_exp(x[3], x[2]);
a = log(Phi_approx(10) - Phi_approx(9));
}If I check out
> out$summary(c("w", "z", "a"))
# A tibble: 3 x 10
variable mean median sd mad q5 q95 rhat ess_bulk ess_tail
<chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 w -Inf -Inf NaN NA -Inf -Inf NA NA NA
2 z -43.6 -43.6 0 0 -43.6 -43.6 NA NA NA
3 a -Inf -Inf NaN NA -Inf -Inf NA NA NALooking at
for (i in 1:40) {
b[i] = normal_lcdf(i | 0, 1);
c[i] = log(Phi_approx(i));
}Shows that the normal_lcdf is more robust
I believe this is a docs issue with the normal distribution. The documentation at
https://mc-stan.org/docs/2_26/functions-reference/normal-distribution.html#normal-distribution says that
Phi_approxis more robust in the tails. However, inspecting this shows that usingnormal_lcdfis actually more robust thanPhi_approx.Description:
Describe the issue as clearly as possible.
If I check out
Looking at
Shows that the normal_lcdf is more robust