Inverse Monte Carlo : Iterative

In this work Y is generated stochastically from a MC transport routine and samples taken from an unknown parameter, $\phi$.

A stochastic method has advantages if little is known about $\phi$ and binning or other parameterisations are difficult. As Y is distributed about $\pi$ and $\phi$, their relationship is now biased.

One solution is to gradually improve the quality of the new estimate Y by increasing the number of histories that contribute to it.

Hence a Monte Carlo method within Markov chain Monte Carlo (McMCMC)?

If the number of histories per iteration, h, is increased linearly then this method converges at a rate, O(1/n^1/4), i.e. really slow!.