Some time ago, I had an ineloquent and less-than-cordial online discussion with a commenter on this site, partially about how statisticians define the term "parameter". This post is just to quote a relevant passage from "Bootstrap Methods and Their Application", by Davison and Hinkley (1997), that better articulates a point I had made earlier. 2.1.1 [...]
That's a mouthful! I presented this topic to a group of Vandy statisticians a few days ago. My notes (essentially reproduced in this post) are recorded at the Dept. of Biostatistics wiki: HowToBootstrapCorrelatedData. The presentation covers some bootstrap strategies for hierarchically structured (correlated) data, but focuses on the multi-stage bootstrap; an extension of that described [...]
A central theme of Don Fraser's article, titled "Is Bayes Posterior just Quick and Dirty Confidence?", was that Bayesian confidence regions have approximate, and sometimes poor frequentist coverage (i.e., the frequency with which a confidence region contains the true parameter value under repeated sampling). Fraser has this warning: The failure to make true assertions with [...]
This popular article references a report by financial consulting firms that makes a fairly convincing argument (even though they mostly neglect inferential statistics, and some parts of their argument are misleading, or otherwise not convincing) that 401(k) participants who accept "help" from financial experts take less risk and have better returns than those who do [...]
The below is taken from a work in progress: The Polya urn is a heuristic associated with Dirichlet process mixtures. We present the scheme in a modified format, using balloons instead of balls, where the probability of drawing a balloon from the urn is proportional to its volume. Balloons are preferred because their volume may [...]
I don't know, of course, because the evidence at hand is based on my experience. But, I'll leave the reader to consider whether these observations generalize. Proponents of Bayesian statistical inference argue that Bayesian credible intervals are more intuitive than the frequentist confidence intervals, because the Bayesian inference is a probability statement about a parameter. [...]
*** Updated 10/27/11: Original text appended in strike. *** Bill Bolstad’s response to Xi’an’s review of his book Understanding Computational Bayesian Statistics included the following comment, which I found interesting: Frequentist p-values are constructed in the parameter dimension using a probability distribution defined only in the observation dimension. Bayesian credible intervals are constructed in the [...]
Antoniak's 1974 article titled Mixtures of Dirichlet Processes with Applications to Bayesian Nonparametric Problems (Annals of Statistics 2(6):1152-1174) is a fundamental work for most modern developments in this area. The article gives two expressions for the expected number of distinct values in a sample of size , drawn from a Dirichlet process-distributed probability distribution with [...]
Here are the 14 slides I used during my talk at the Joint Statistical Meetings 2011: shotwell-jsm-2011.pdf. I’m trying hard to minimize the text in my presentation slides. But, this usually requires that I practice more. Hence, you will know which talks I have practiced thoroughly by the amount of text in the slides . [...]
Also in this picture: Mary Shotwell, PhD (right) and our Mentor Elizabeth Slate, PhD (left)
