Ranking and selection with unknown correlation structures

Abstract

We create the first computationally tractable Bayesian statistical model for learning unknown correlations among estimated alternatives in fully sequential ranking and selection. Although correlations allow us to extract more information from each individual simulation, the correlation structure is itself unknown, and we face the additional challenge of simultaneously learning the unknown values and unknown correlations from simulation. We derive a Bayesian procedure that allocates simulations based on the value of information, thus exploiting the correlation structure and anticipating future changes to our beliefs about the correlations. We test the model and algorithm in a simulation study motivated by the problem of optimal wind farm placement, and obtain encouraging empirical results.