Inverse Monte Carlo: Non-iterative

It is usually the case that $\pi$ is not directly samplable, otherwise McMC would be trivial so other methods such as importance sample are probably more appropriate.

Y might be computed as a deterministic function of an unknown parameter, $\phi$, in which case McMC can be used to invert the relationship between $\phi$ and $\pi$.

This is the basis of simulated annealing, a useful technique for dealing with non-linear constraints such as positivity.