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Bayesian statistical models can be used to represent the beliefs of a decision-maker about an uncertain environment. For example, in revenue management, a seller formulates beliefs about customers' willingness to pay; in energy, we may have a belief about the suitability of a candidate location for a new wind farm. Conjugate priors model the evolution of these beliefs over time as new information is collected, either from stochastic simulation or field experiments. However, there are relatively few of these conjugate models, and they simply do not exist in many problems of interest. We show how approximate Bayesian inference can be used to create computationally tractable, "nearly conjugate" models that optimally approximate the actual belief distributions and enable the use of anticipatory information collection and optimization policies. We consider two broad problem classes: simulation selection with unknown correlation structures, and Bayesian learning in logistic regression.
Ilya O. Ryzhov is an Assistant Professor in the Department of Decision, Operations, and Information Technologies in the Robert H. Smith School of Business, University of Maryland. He received a Ph.D. in Operations Research and Financial Engineering from Princeton University in 2011. His work deals with the collection and valuation of information in stochastic optimization, with applications in non-profit analytics, energy, and operations management.
He is a coauthor of the book Optimal Learning (Wiley, 2012).