P.Mean: Can Bayesian methods help with small sample sizes?  (created 2011-04-20). News: Sign up for "The Monthly Mean," the newsletter that dares to call itself average, www.pmean.com/news.

I'm a big fan of Bayesian methods, but I had to intervene on the "wrong" side in a debate over methodology for small sample sizes. Thanks to Mark Powell for your interesting reply. I am a big fan of Bayesian methods and have a section of my website devoted to this topic: * http://www.pmean.com/category/BayesianStatistics.html I also have an interest in applying Bayesian methods in a novel area, predicting accrual rates in a clinical trial. * http://www.pmean.com/category/AccrualProblems.html There is a link on this page to my old website * http://www.childrensmercy.org/stats/weblog2007/CaseStudyOfAccrualPart2.asp an example there where accrual is so slow that only five patients appear in the first six weeks of observations (three patients per week were expected). So the use of a prior distribution (note: an INFORMATIVE prior distribution) is absolutely vital in this example. That being said, I don't see Bayesian methods as being able to squeeze blood from a turnip. If there is a small sample size, Bayesian methods won't magically teleport you to the land where all your estimates are tightly bounded and all your decisions are obvious. One of your decisions, of course, should be to defer any decisions until you have more data, and Bayesian methods can certainly help lead you down this path with small sample sizes. I'm just afraid that your natural enthusiasm will give people falsely high expectations of what these methods are capable of doing. There's a practical reason here also. The people who produce really small sample sizes are probably not the best people to spring new methodologies on. So, yes, I share your enthusiasm for Bayesian methods, but I would still urge caution in introducing this to solve problems with small sample sizes.

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