I need to use the 10 dimensional normal CDF inside Stan. Given that Stan only officially supports the one-dimensional normal CDF, I wonder what my options are?
E.g., is numerical integration possible for my purpose? Is it possible to implement some algorithm that underlies the multivariate normal CDF packages in R or other languages (like the mvtnorm package) (which I’m willing to do myself)?
I have used a 2-dimensional normal CDF inside Stan with the help of a code circulated on this forum. But according to some post on this forum dated several years ago, one reason Stan doesn’t have higher-dimensional normal CDF is the lack of a deterministic way to calculate normal CDF. However, my current project does require me to use a 10-dimensional normal CDF, and I don’t think there is a way to reduce the dimension (because all elements of the 10-dimensional covariance matrix are not zero). If I don’t need the CDF to be super precise or deterministic, would that open up some possibilities for implementing the CDF?
Any suggestion is greatly appreciated! Thank you!