Exercises for Mon Oct 6: ¡­

Exercises for Mon Oct 6:

First: the rest of Exercise 2.13.

Then: go to http://lib.stat.cmu.edu/DASL/Stories/EstimatingtheSpeedofLight.html to find the 66 speed of light measurements from 1882, described in the book's Section 3.2. Assuming the normal (mu, sigma^2) model for these, apply the prior that takes sigma^2 an Inv-Gamma (1,10) and mu for given sigma a Normal (20, sigma^2/0.33^2). Simulate 10^5 realisations (mu, sigma) from the posterior. Give point estimates and 95% credibility intervals for mu, for sigma, and for the probability alpha that a new measurement will fall to the left of 12.5.

Then: redo the above with a more carefully constructed prior for sigma: let sigma^2 be Inv-Gamma (a,b), with parameters to reflect 0.10 prior quantile equal to 2.2 and 0.90 prior quantile equal to 18.8, for sigma.

Then: Exercises 17 and 22 from Ch 2, and 2 and 4 from Ch 3.