I got an email asking for a recommendation for an introductory book on Bayesian Statistics from someone who recently graduated from our program. It’s kind of a difficult request because the mathematical demands needed to understand Bayesian statistics are not trivial. Here’s what I recommended. Continue reading

# Tag Archives: Bayesian statistics

# PMean: Too many different prior choices for the hierarchical beta binomial model

I’m interested in studying how Bayesian hierarchical models work and I want to start with what seems like the simplest case, the hierarchical beta-binomial model. It’s actually not that simple, it seems. There are too many choices for the hyperprior that you use in this setting. Continue reading

# Recommended: Bayesian computing with INLA

This page promotes a new approach to a broad class of models (spatio-temporal models, latent variable models, mixed models) using a fast approximation to the Bayesian solution. It runs under R and appears to handle very large datasets. I have not had a chance to try this, but it looks very interesting. Continue reading

# Recommended: Editorial (Basic and Applied Social Psychology)

Recommended does not always mean that I agree with what’s written. In this case, it means that this is something that is important to read because it offers an important perspective. And this editorial offers the perspective that all p-values and all confidence intervals are so fatally flawed that they are banned from all future publications in this journal. The editorial goes further to criticize most Bayesian methods because of the problems with the “Laplacian assumption.” The editorial authors have trouble with some of the ambiguities associated with creating a non-informative prior distribution that is, a prior distribution that represents a “state of ignorance.” They will accept Bayesian analyses on a case by case basis. Throwing out most Bayesian analyses, all p-values, and all confidence intervals makes you wonder what they will accept. They suggest larger than typical sample sizes, strong descriptive statistics (which they fail to define), and effect sizes. They believe that by “banning the NHSTP will have the effect of increasing the quality of submitted manuscripts by liberating authors from the stultified structure of NHSTP thinking thereby eliminating an important obstacle to creative thinking.” It’s worth debating this issue, though I think that these recommendations are far too extreme. Continue reading

# PMean: What is the probability of a probability of one

Someone wrote asking me about a variation of the “Rule of Three”. This rule says that if you observe zero events out of n, an upper 95% confidence limit for n is approximately 3/n. So suppose you operated on 10 patients and none of them died after surgery. Then you would be 95% confident that the mortality rate would be 30% (3/10) or less. This person asked “Suppose I repeatedly sample from a population and every patient in the sample was a G. What is the how likely is it that the entire population is Gs?” This flips the problem around, and is equivalent to saying that the probability of survival is 97% or greater. But this person wanted an estimate of the probability that the probability in the population is 1. Continue reading

# PMean: Using BUGS within the R programming environment

I am giving a talk today for the Kansas City R Users group about BUGS (Bayes Using Gibbs Sampler). I have already written extensively about BUGS and the interface to BUGS from within the R programming environment, and you can find these on my category page for Bayesian statistics. Here is a quick overview of why you might want to use BUGS and how you would use it. I’ve included links to the relevant pages on my website so you can explore this topic further on your own. Continue reading

# PMean: Is Possibility Theory better than Probability Theory?

Someone on a LinkedIn group posted a question about “Possibility Theory.” The question itself had a lot of hype, claiming that “time has expired for Probability Theory.” Still, it is an interesting question and here’s how I responded. Continue reading

# PMean: The cost of a bad prediction

Paul Krugman wrote up an interesting application of Bayes Theorem on his blog on the New York Times. I want to adapt his example and expand it a bit. Continue reading

# Recommended: Revised standards for statistical evidence

This article compares the Bayesian standard of what constitutes convincing evidence to the frequentist reliance on the p-value to measure evidence. The author concludes that a much smaller p-value (0.005 or 0.001) is needed to be consistent with the Bayesian standard. Continue reading