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This course will consist of two parts: a morning session on Monte Carlo integration strategies and an afternoon session on optimization methods. We will survey a variety of techniques, ranging from classic to state-of-the-art. The course will be based on the book ``Computational Statistics'', by Givens and Hoeting (Wiley), which covers these and other topics in greater detail. Many problems in statistics require the evaluation of integrals that cannot be solved analytically, particularly in Bayesian statistics. In the morning session we will cover Monte Carlo integration, importance sampling and variance reduction techniques, and Markov chain Monte Carlo methods. Optimization also plays a central role in statistics, particularly in numerical maximum likelihood estimation. The afternoon session will focus on various optimization strategies including Newton-like methods, Gauss-Seidel iteration, tabu algorithms, simulated annealing, genetic algorithms, the EM algorithm and its variants. We seek to give students a practical understanding of how and why existing methods work, enabling students to use modern statistical methods effectively. Examples are drawn from diverse fields including bioinformatics, ecology, and medicine. The course is targeted for quantitative scientists and statisticians who are unfamiliar with these methods. Upper division undergraduate mathematical literacy is recommended. No computer programming experience is necessary. OPTIONAL TEXTBOOK AVAILABLE
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