I would like to transform a parameter by a Gaussian CDF with variance 5. Should I just use normal_cdf(theta,0,5) or is there a way to use Phi_approx which I assume is faster and more robust?
If you do Phi_approx(theta / sqrt(5)); that is approximately the same thing as normal_cdf(theta, 0, 5) iff theta is a scalar. But the Gaussian CDF is not all that slow to evaluate, so I doubt changing it is going to make much of a difference.
Phi_approx(theta / sqrt(5));
normal_cdf(theta, 0, 5)