Monte Carlo Simulation for Statistical Inference, Model Selection and Decision Making
The first part of his course will consist of two presentations. In the first presentation, he will introduce fundamentals of Monte Carlo simulation for statistical inference, with emphasis on algorithms such as importance sampling, particle filtering and smoothing for dynamic models, Markov chain Monte Carlo, Gibbs and Metropolis-Hastings, blocking and mixtures of MCMC kernels, Monte Carlo EM, sequential Monte Carlo for static models, auxiliary variable methods (Swedsen-Wang, hybrid Monte Carlo and slice sampling), and adaptive MCMC. The algorithms will be illustrated with several examples: image tracking, robotics, image annotation, probabilistic graphical models, and music analysis.
The second presentation will target model selection and decision making problems. He will describe the reversible-jump MCMC algorithm and illustrate it with application to simple mixture models and nonlinear regression with an unknown number of basis functions. He will show how to apply this algorithm to general Markov decision processes (MDPs). The course will also cover other Monte Carlo simulation methods for partially observed Markov decision processes (POMDPs) using policy gradients, common random number generation, and active exploration with Gaussian processes. An outline to some applications of these methods to robotics and the design of computer game architectures will be given. The presentation will end with the problem of Monte Carlo simulation for Bayesian nonlinear experimental design, with application to financial modeling, robot exploration, drug treatments, dynamic sensor networks, optimal measurement and active vision.
Author: Nando De Freitas, University Of British Columbia