演講公告 89年5月17日 (星期三)

摘要

Random Number Generation For The New Century (based on a paper to appear in The American Statistician, May, 2000) We will review some classical uniform random number generators and two recent extensions. The matrix congruential generator (MCG) is a multivariate extension of the classic Linear Congruential Generator (LCG). The multiple recursive generator (MRG) is another extension based on a k-th degree primitive polynomial over a large finite field. A simple and efficient construction algorithm is presented. They are compared with the classical generator LCG. It is shown that MRG/MCG is a much better random number generator than the popular LCG. A special form of MRG/MCG is constructed and recommended as the random number generator for the new century. A step-by-step procedure for constructing such a random number generator is also provided. Markov Chain Monte Carlo: Metropolis Algorithm, Gibbs Sampling and Some Applications. In this talk, we will start with an example, Genetic Linkage Model, to motivate various Markov Chain Monte Carlo (MCMC) methods. In particular, we will use the example to illustrate the use of EM algorithm, Metropolis algorithm, and Metropolis-Hastings Method. We will discuss their connection with the standard Rejection method in random variate generation. Finally, we give another example to illustrate the foundation, the procedure and some applications of Gibbs sampling.