I have a pretty general question and I would really appreciate if you give me any hints or point me towards some relevant literature.
Suppose $X$ is an $n$-dimensional Gaussian vector.
What is the conditional distribution $\left[X|f(X)\right]$, where $f(X)$ is a non-linear function of the coordinates of $X$? Are there any results/methods that deal with that kind of problems?
Thank you!