I am just getting started in julia, and there seem to be many options for doing bayesian inference. I have been looking at Mamba and Klara, but I am not sure which is better for what I want to do: inference using continuous time Markov processes observed at discrete intervals.

In this scenario, writing the likelihood function requires a matrix exponential function. HMC would then require computing the derivatives of the matrix exponential in a numerically stable fashion. This is apparently not a trivial thing to do (see this STAN issue: github (https://github.com/stan-dev/math/issues/32). Has anybody here used julia for my application?