> I wonder if the tricky part is in choosing random vectors? Sampling vectors from multidimensional random distributions is a well studied problem. For exampl

> I wonder if the tricky part is in choosing random vectors? Sampling vectors from multidimensional random distributions is a well studied problem. For example the open source project https://mc-stan.org https://mc-stan.org implemented several (at the time) state of the art methods like Hamiltonian Monte Carlo with the help of Automatic Differentiation.