Exercises for Friday September 21
- On Friday 14th of September we went through Chapter 4, with particular emphasis on the lazy Bayes (and half lazy Bayes) strategies. I also went through exercises with some details: the remaining parts of exercise 1 from exam project 2015, Nils Ex 13 e), f) and g) and Nils Ex 14 a). Nils Exercises 14 b) and 22 will be treated next time.
- Next week we will start discussing Bayesian Computation, the theme of Chapters 10 and 11.
- Note the three new R-scripts (on the right) which contains R-solutions for exercise 1 from exam project 2015 (a new version) and Nils Exercises 14 and 22.
- Exercises:
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Small Mixture Prior exercise (coin flipping): you flip a coin n = 25 times and observe y = 10 Heads. Find the posterior density of theta = Pr(head), along with "standard summary numbers", namely posterior mean, posterior standard deviation, 0.05, 0.50, 0.95 posterior quantiles, for each of the following priors:
(a) theta is uniform on (0,1) (which is where Thomas Bayes started, in 1763).
(b) theta is a Beta(c,c), with a high c, like c = 100.
(c) theta is a mixure 0.50 * uniform + 0.50 * Beta(c,c).
(d) theta is a mixture 0.50 * uniform + 0.50 * unit-point-mass-at-0.50.
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Finish exercises from last time (if you did not do them last week).
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Nils Exercise 9 e) (read through the rest of Exercise 9, you should be able to use the theory described there, but you do not need to work through the details).
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