Category: Bayesian statistics

Category: Bayesian statistics. In Bayesian statistics, the researcher specifies a probability distribution prior to the start of the experiment that represents his/her degree of belief about the possible values of a process being studied. After data is collected, the Bayesian analysis produces a posterior distribution that combines information from data with information from the prior distribution. Articles are arranged by date with the most recent entries at the top. You can find the theme and closely related categories and other resources at the bottom of this page.

Stats: Eliciting a prior distribution for rejection/refusal rates (June 7, 2008). I got a question about the Bayesian model for rejection/refusal rates. I had used three prior distributions in my calculations, a Beta(10,40), a Beta(45,5), and a Beta(25,25). The question was, how did I select those prior distributions.

Stats: Why does a Bayesian approach make sense for monitoring accrual? (May 8, 2008). I'm working with Byron Gajewski to develop some models for monitoring the progress of clinical trials. Too many researchers overpromise and undeliver on the planned sample size and the planned completion date of their research This leads to serious delays in the research and inadequate precision and power when the research is completed. We want to develop some tools that will let researchers plan the pattern of patient accrual in their studies. These tools will also let the researchers carefully monitor the progress of their studies and let them take action quickly if accrual rates are suffering. We've adopted a Bayesian approach for these tools. While a Bayesian approach to Statistics is controversial, we feel that there should be no controversy with regard to using Bayesian models in modeling accrual.

Stats: Fitting a beta binomial model using BUGS (April 17, 2007). I've spent a bit of time trying to learn how to run a program called BUGS. The acronym stands for Bayes Using Gibbs Sampling. Here is my first serious attempt to run a BUGS program.

Stats: A simple illustration of the Metropolis algorithm (April 13, 2007). In many situations, you need to generate a random sample from a distribution that is rather complex. When simpler methods for generating a random sample don't work, there are a series of approaches based on the Markov chain principle that can help. There are several of these methods: Gibbs sampling, the Metropolis algorithm, the Metropolis-Hastings algorithm, that are collectively called Markov Chain Monte Carlo (MCMC). These approaches are especially valuable in Bayesian data analysis. The simplest of the three methods is the Metropolis algorithm, and here is a simple example of how it works.

Stats: What I'm working on right now (March 18, 2007). There are several research projects where I am actively looking for collaborators. I thought I'd outline these topics briefly here.

Stats: A simple Bayesian model for accrual (November 17, 2006). Suppose you are a researcher in charge of a long term study. You plan to collect data on 120 patients. The goal is to finish your study in ten years, which means getting 12 patients per year or one every thirty days on average. Recruiting patients though appears to be harder than you had expected. You recruited your first patient on day 56, 26 days behind schedule. The second patient is not recruited until day 93. About two years into the study (day 768), you have just recruited your 10th patient. It looks like recruitment might be behind schedule. Is it time to take action? A Bayesian model of accrual times can help you to discern whether recruitment is behind schedule and project an estimated completion date allowing for uncertainty.

Stats: Articles on Bayesian data analysis (March 30, 2006). The Journal of Data Science has a couple of interesting Bayesian papers in the April 2006 issue. The first article addresses a thorny topic, multiple comparisons in an ANOVA model. The second article discusses the teaching of Bayesian statistics.

Stats: Technology to end spam (March 8, 2005). In my job I get a lot of spam, partly because I listed my email address on my web site until just recently. The research community is trying to find technological solutions to spam (unsolicited commercial email), and some of the approaches are quite fascinating. The folks at Microsoft have looked at a system that limits the amount of email that someone can send out in a single day by asking the sender to solve a moderately difficult computational challenge for each piece of email sent. Another interesting approach uses Bayesian Statistics to produce a probability estimate that the message is spam. This approach looks at words that appear commonly in spam messages and uncommonly in legitimate messages.

Stats: Steps in a typical Bayesian model (January 24, 2005). I editorialized a year ago about this on the evidence-based Health List. "Should proponents of EBM be concerned about understanding the Bayesian philosophy? In my opinion, no. I think we'll gradually see Bayesian philosophy creep in to the design and analysis of clinical trials. For example, there are good Bayesian solutions, I understand, to the tricky issue of early stopping of clinical trials. But I doubt that we will see a wholesale rejection of both p-values AND confidence intervals in my lifetime. Too many people like me fail to fully understand the Bayesian paradigm for this to happen. So from a practical viewpoint, most of the medical research for the foreseeable future will be analyzed using the Frequentist paradigm."

Theme and closely related categories:

Other resources:

Bayesian Models for Gene Expression With DNA Microarray Description: This article presents a Bayesian selection criteria for identifying a small set of genes that can distinguish between different types of tissue.
Decision theoretic designs for Phase II clinical trials with multiple outcomes. Description: This article provides a Bayesian approach to handling multiple comparisons in a trial where with multiple safety and efficacy endpoints.
Empirical-Bayes adjustments for multiple comparisons are sometimes useful. Description: This article proposes situations where adjustments for multiple comparisons are appropriate. The authors offer Empirical-Bayes and fully Bayesian approaches and describe their advantages over the traditional Bonferroni approach.
Overview of Computer Intensive Statistical Inference Procedures. Description: This page provides a nice overview of the permutation test, randomization test, Monte Carlo estimation, bootstrapping, the jackknife, and Markov Chain Monte Carlo methods.

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This webpage was written on 2007-05-30 and was last modified on 2008-07-08.