exercises for Wed Sep 22
1. On Wed Sep 15 we rounded off Ch 2, and started gently on Ch 3. We also went through extra exercises (i), (ii), (iii), (iv), and learned more about marginal distributions, predicitive distributions, the multinormal distribution, the Jeffreys prior, etc.
2. Nils Exercise 9 is defined as ten-minute curriculum about the multinormal distribution, with formulas for conditional distributions; these will be used in various setups later in the course.
3. Exercises for Wed Sep 22:
(i) Suppose (a,b) are unknown parameters, with a binormal prior, with prior means (a_0,b_0) = (3.0, 2.0), prior standard deviations (1,0.5), and prior correlation 0.66. What is the prior probability that a > b? Then we observe (x,y), which for given (a,b) is a binormal with mean (a,b), variances 1, 1, and correlation 0.33. With (x,y) = (2.77, 2.33), find the posterior distribution for (a,b). What is now the probability that a > b?
(ii) Nils Exercise 14, Gott würfelt nicht.
(iii) BDA Ch 3 Exercises 2, 7. Look also at Exercise 8, which we'll a little bit later, to see the scope of applicability of what we're learning in Ch 3.