Augmented Markov Chain Monte Carlo Simulation for Two-Stage Stochastic Programs with Recourse

In this paper, we develop a simulation-based approach for two-stage stochastic programs with recourse. We construct an augmented probability model with stochastic shocks and decision variables. Simulating from the augmented probability model solves for the expected recourse function and the optimal first-stage decision. Markov chain Monte Carlo methods, together with ergodic averaging, provide a framework to compute the optimal solution. We illustrate our methodology via the two-stage newsvendor problem with unimodal and bimodal continuous uncertainty. Finally, we present performance comparisons of our algorithm and the sample average approximation method. About the Speaker Nicholas Polson is a Bayesian statistician who conducts research on Financial Econometrics, Markov chain Monte Carlo, Particle learning, and Bayesian inference. Inspired by an interest in probability, Polson has developed a number of new algorithms and applied them to the fields of statistics and financial econometrics, including the Bayesian analysis of stochastic volatility models and sequential particle learning for statistical inference. Polson’s article, “Bayesian Analysis of Stochastic Volatility Models,” was named one of the most influential articles in the 20th anniversary issue of the Journal of Business and Economic Statistics. His recent work includes methods for sparse Bayesian estimation with application to high dimensional regression and classification. Enquiry: 3442 8408 All are Welcome! SEEM Seminar 2014-2015/028