Stan and PyMC3 both implement automatic differentiation based variational inference, so you can write down your statistical model and not care "much" about derivatives.<p><a href="http://mc-stan.org" rel="nofollow">http://mc-stan.org</a>
<a href="https://github.com/pymc-devs/pymc3" rel="nofollow">https://github.com/pymc-devs/pymc3</a>
> Many samples needed, especially in high dimensions<p>This isn't true. For Monte Carlo sampling, the convergence of unbiased estimators (for example the expectation) is independent of the dimension of the state space. In fact, this is exactly the reason to <i>prefer</i> Monte Carlo integration over, say, a Riemann sum.