Dr. Louis Lyons (Oxford, UK) Date: Mar. 22, 2009 Title: Bayes versus Frequentism - the return of an old controversy Abstract: The Bayes and Frequentist methods for determining parameters and for various other statistical procedures are based on very different philosophies. This colloquium explains the differences in these approaches, with examples both from Physics and from every-day life. One situation in which they can give different results is the extraction of upper limits when a sought-for signal is not seen. The Feldman-Cousins approach to this problem is discussed. Finally a summary is presented, contrasting these approaches.