The workshop will be held January 18-19, 2013, on the campus of the University of Florida. Although Monte Carlo methods have existed for a long time, the problems to which they are applied have changed dramatically. Monte Carlo methods are now routinely applied to very complex problems, for instance Bayesian regression models with a large number of predictors and Bayesian hierarchical models involving many levels. To address this increased complexity, recent research on Monte Carlo approaches has proceeded in several new directions. For example, because in highly complex models it is no longer possible to analytically devise Monte Carlo algorithms which are optimal or near-optimal, researchers have developed "adaptive MCMC algorithms" which, as they are running, automatically evolve into algorithms which are optimal for the current problem. Another example involves Bayesian model selection, where researchers have many models that can be used to explain the data, and they wish to select the best one. In a Bayesian approach, a prior is placed on the set of potential models, and the researcher wishes to obtain the posterior distribution of the models, and the parameters for the models. Because the parameters for the different models may have different dimensions, Markov chains for estimating posterior distributions must be "transdimensional." In this workshop, twelve distinguished individuals who work in Monte Carlo simulation review the current state of the field and present their recent work. A number of young researchers will also participate in the workshop and present their work in poster sessions.
Monte Carlo simulation is a methodology that uses random sampling to arrive at numerical approximations to quantities that cannot be computed exactly. The methodology allows researchers to use extremely complex statistical models: if a potentially useful model is so complicated that it is not possible to obtain exact solutions, the model can still be considered if one is willing to use approximate solutions provided by Monte Carlo simulation. Recent advances in computing power have made Monte Carlo simulation increasingly accurate and useful, but many unsolved problems remain. The workshop provides an excellent opportunity for established researchers in the field, as well as newcomers, to discuss the significant developments that have taken place in the last decade; to discuss what works and what does not; and to identify important problems and new research directions.
Monte Carlo simulation is a methodology that uses random sampling to arrive at numerical approximations to quantities that cannot be computed exactly. The methodology allows researchers to use extremely complex statistical models: if a potentially useful model is so complicated that it is not possible to obtain exact solutions, the model can still be considered if one is willing to use approximate solutions provided by Monte Carlo simulation. Recent advances in computing power have made Monte Carlo simulation increasingly accurate and useful, but many unsolved problems remain. The purpose of the workshop was to provide an opportunity for established researchers in the field, as well newcomers, to discuss the significant developments that have taken place in the last decade; to discuss what works and what does not; and to identify important problems and new research directions. The workshop generated and stimulated interest in important new directions in Monte Carlo methods among researchers nationwide, particularly among young researchers and graduate students, at the University of Florida and at other universities in the country, and promoted future collaborations among researchers. In addition, the interaction with the senior researchers was very helpful to the young people who are striving to establish themselves in statistical research. Many of the methods developed for statistical applications (for example in Bayesian analysis) wind up being useful in other disciplines. For example, regenerative Monte Carlo methods, originally developed for Bayesian problems, are now being used for problems involving the simulation of quantum systems in physics.
