STAT 330 November 8, 2011

Here is the link to the VPN client mentioned in class today, that allows you to connect to websites as if you were on campus.

Here are the links to the papers I mentioned this morning. First the paper by Berger and Delampady. Next, the paper by Berger and Sellke. And finally, the link to Jim Berger’s website with the Java Applet that allows you to try the thought experiment I discussed in class. The URLs for the first two have changed as jstor.org has changed their method of assigning stable URLs.

Finally, here is a link to the paper by Dellaportas, Forster and Ntzoufras, on reversible jump MCMC.

It appears that Romney has conceded Florida. This comment to today’s Nate Silver blog is very cool (difference between mean and mode).

Here’s a cartoon about frequentism vs. Bayesianism. Don’t take it too seriously. If you mouse over the picture, a hidden message appears.

I pointed out some shortcomings of classical hypothesis tests and p-values. I then outlined how Bayesian tests might be conducted, first in the context of two simple hypotheses and then in the context of one simple and one complex hypothesis. In the latter case there is an additional parameter \theta which requires a prior. Then to consider just the two hypotheses we have to marginalize the posterior probability on the complex hypothesis with respect to \theta.

I pointed out that the results will depend sensitively on the prior, which means that Bayesian hypothesis tests must be conducted with great care. There are some results that are more robust with respect to the prior, and we will discuss them in subsequent classes. I showed an example (biased coin) and demonstrated that the results of a Bayesian hypothesis test can be very different from frequentist ones.

I briefly outlined how reversible jump MCMC can be used to evaluate the posterior probabilities of hypotheses. I’ll show you a program on Tuesday to make this more concrete. I mentioned that the same ideas can be used to compare multiple models of various number of parameters.

I discussed some other problems with p-values, in particular that they overstate the evidence against the null. I pointed to Jim Berger’s website for the Java applet (link above).

I finished with the beginning of a discussion of philosophical issues that relate to Bayesian epistemology.

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