STAT 330 October 11, 2012

Here is the next problem set, due on Thursday, October 18.

Here is the next chart set, on Normal Linear Models.

If you are interested in more about Nate Silver, whom I mentioned a few days ago, he was interviewed on the NPR show “Fresh Air” yesterday. You can listen to the interview here.

NEW: Here’s an interesting article about Bayes and children, who may start out as natural Bayesian processors. It mentions Nate Silver.

Today we looked at the simulations for the normal inference problem we discussed last time. I fixed the code by removing the offending invisible character (I’ve posted the code already). We looked at two versions, one of which sampled on \mu and \sigma separately, and the other that sampled them simultaneously. I pointed out that the second example might not sample quite as well with the same values of a and b, but might be competitive if they were somewhat smaller; I also noted that the second example evaluates the likelihood function half as many times as the first solution. This could be important in cases where the likelihood is expensive to compute.

We then resumed discussion of the Poisson distribution. We noted that in realistic cases, we may have to evaluate both a signal (the brightness of a star, for example) and a noisy background (due to a collection of very faint and more distant stars near the one we are studying, for example). The straightforward method would be to measure star+background=s+b=u, and then move the telescope off of the star to measure background=b by itself. Then we would subtract b from u to get s. If the signals are large, this works well; but if they are small it is statistically possible to measure b>u which would result in s<0, which is unphysical.

We developed a method for doing this, and simulated it by sampling.

Here is a link to the code for sampling in this problem.

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