We started by looking at the natural frequencies interpretation of the remark made by Alan Dershowitz, O. J. Simpson’s attorney, and got the same results we got by solving Bayes’ theorem directly. We then proceeded to look at three different problems involving sampling: Sampling with replacement (testing parts), sampling without replacement (polling voters) and a catch-and-release problem. In the first of these, the samples are independent, but in the other two they are dependent and care must be taken to assure a correct likelihood function. We concluded this chart set by seeing how R can be used to draw the posterior distribution of the voting example, and then how the same problem can be solved by sampling and then using the sample to compute credible intervals, means, medians, variances, standard deviations, and so forth.

We continued with the discussion of the next chart set: How to interpret the posterior probability. We discussed Bayesian credible intervals; I also briefly discussed means, medians and modes in terms of loss functions and decision theory.

People asked when the first problem set will be assigned. I expect to hand out a problem set on Tuesday.

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