< br>In this talk we describe the Multi-Index Stocha stic Collocation method (MISC) for computing stati stics of the solution of an elliptic PDE with rand om data. MISC is a combination technique based on mixed differences of spatial approximations and qu adratures over the space of random data. We propos e an optimization procedure to select the most eff ective mixed differences to include in the MISC es timator: such optimization is a crucial step and a llows us to build a method that\, provided with su fficient solution regularity\, is potentially more effective than other multi-level collocation meth ods already available in literature. We provide a complexity analysis both in the case of a finite a nd an infinite number of random variables\, showin g that in the optimal case the convergence rate of MISC is only dictated by the convergence of the d eterministic solver applied to a one dimensional p roblem. We show the effectiveness of MISC with som e computational tests\, and in particular we discu ss how MISC can be efficiently combined with an is ogeometric solver for PDE. LOCATION:Seminar Room 1\, Newton Institute CONTACT:INI IT END:VEVENT END:VCALENDAR