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Value of information methods for pairwise sampling with correlations

We consider optimization via simulation over a finite set of alternatives. We employ a Bayesian value-of-information approach in which we allow both correlated prior beliefs on the sampling means and correlated sampling. Correlation in the prior belief allow us to learn about an alternative's value from samples of similar alternatives. Correlation in sampling, achieved through common random numbers, allows us to reduce the variance in comparing one alternative to another. We allow for a more general combination of both types of correlation than has been offered previously in the Bayesian ranking and selection literature. We do so by giving an exact expression for the value of information for sampling the difference between a pair of alternatives, and derive new knowledge-gradient methods based on this valuation.