With the development of computers, simulation is now a frequently used method for solving problems in business, in the physical and social sciences, in engineering, in operations research, and in statistics. Simulation is best regarded as mathematical experimentation, and needs all the care and planning that are regarded as a normal part of training in experimental sciences. However, many simulation studies lack a thorough statistical design and analysis. Thus, one purpose of this course will be to make students more aware of the statistical aspects of simulation and give them a working knowledge of the statistical techniques involved. Much is possible in the way of design because randomness is introduced by the experimenter and hence is under his or her complete control. Techniques described under the heading of variance reduction will be discussed.
A second purpose of this course is to discuss how statistics itself makes use of simulation. One such use involves the investigation of the sampling distribution of an estimator and its possible robustness. Two other uses, for example, are the computation of the resampling distribution employed in bootstrap methods, and Gibbs sampling in Bayesian analysis.
It would be desirable for students to have completed or to be at least taking concurrently MATH3131.03.
The text will probably be B. J. T. Morgan, Elements of Simulation (Chapman and Hall).
The final grade may be based on assignments, a class test, a project, and a final examination.