Multi index methods are based on Sparse Grid methods and utilize the extra mixed regularity between dimensions (spatial or stochastic) to reduce the work complexity of different methods. In fact, in some cases we may get the rate of work complexity that is independent of the number of dimensions. We have developed a Mutli Index variant of the Monte Carlo (MIMC) method and we are currently developing a Multi Index variant of the Stochastic Collocation (MISC) method.
Multi Index Monte Carlo: When Sparsity Meets Sampling, Numerische Mathematik, pp 1-40, June 2015.