exercises for Week 5 (Mon Sep 15 ff) and Week 6 (Mon Sep 22 ff)

Mon Sep 22 & Wed Sep 24: 

Exam 2015, #4 uniform with a prior
Exam project 2010. #1 Myshkin kabal 

More Jeffreys and vip-Jeffreys: 7.26, 7.29, 7.30.

Mon Sep 15 & Wed Sep 17: Story #17 cigarettes (Bayesian part); normal-normal and gamma-normal things 7.19, 7.21; then Jeffreys 7.25, 7.26, and soon enough vip-Jeffreys exercises 7.29.

You should also do this, a simplified version of the cigarettes problem: generate n = 100 datapoints from y = \beta x + \eps, for some true \beta_0, with the x_i and \eps_i standard normal. The prior for \beta is flat on [0,\infty) (i.e. we do not tolerate \beta negative). Code up an MCMC doing this, and check how \beta given data looks, for true \beta_0 clearly positive; for \beta_0 close to zero; and for \beta_0 a bit negative. 

We'll also do more of earlier exam, exam projects, oblig exercises soon, and the next to work through here are: 
   Exam 2017, #3 blood on the tracks 
   Exam 2015, #4 uniform with a prior 
   Exam project 2015, #3 Poisson breakpoint British mining