exercises for Tue Sep 17

1. On Tue Sep 10 we went into various aspects of the Dirichlet process, regarding construction, existence, interpretation, simulation ("brute force" via lots of boxes, and also stick-breaking), prior to posterior updating. We also discussed bits & pieces of Exercises 4, 5, 6, 7, 8.

2. I've uploaded R scripts com43a (for Gott würfelt nicht, kann es der wahre Jacob sein?) and com44a (for the Nils VIE Very Important Exercise 8, with simulations for prior and posterior Dirichlet processes). Copy them, use them, check their steps, play with other parameter values, etc., and be able to modify them.

3. Next week we do more on the Dirichlet processes, including also modelling setups where the Dirichlet process generate parameters, as opposed to generating data directly.

4. Exercises for Tue Sep 17: First do the following simple extra exercise. y is binomial (n, \theta), and \theta has the interesting prior 0.50*uniform + 0.50*\delta(0.50), the second component being a unit pointmass at position 0.50 -- either my coin is completely plain and standard, or it is totally strange with me knowning nothing at all about its \theta. Work through Bayes things for this setup, and illustrate, with a clear picture of the posterior for \theta, with e.g. n = 20 and y = 13. Do this also via the approximation which takes 0.50*uniform + 0.50*Beta(c,c) with c = 1000. Do the math to see that c going to infinity gives the right answers.

Then do the rest for Nils Exercise 4(b). Then the VIE Exercise 9, with 51 horrible big wars since 1823, 37 before Vietnam and 14 after. Invent your own context-relevant focus parameter, and present an analysis for that parameter. Are you with Pinker (and Celine and Nils), or not?
https://twitter.com/sapinker/status/952978002085892096?lang=en