What is the guidance around user-supplied (deterministic) initial values? When is it a good idea?

In principle you need randomness of the initial values to make sure your model is robust and converges despite different initial starting points.

Setting them could be useful (not limited to):

- speeding up the model in case some parameters are far from the interval -2+2
- stability issue in some cases (when cumulative distributions are used)

thanks ! what is the relevant literature or documentation about this?

to quote @betanalpha on this from another post. I suggested setting initial values to the maximum a posteriori values (mode of the posterior distribution) discovered by some cheaper EM algorithm, in order to assist MCMC convergence. He replied as follows.