Exercises for Mon 25 Jan

Today, Mon 18 Jan, I gave a broad introduction to the course and went through some of the practicalities. I also discussed some of the issues laid out in the CLP book's chapter 1. Again, please print out the material on the website for yourself. There will also be some lectures notes & exercises placed at the site a bit later. 

For Mon 25 Jan, do the following exercises. First, go to the Claeskens and Hjort Model Selection book website and access the lifelengths dataset for 82 men and 59 women from Roman era Egypt (c. 100 years b.C.). Redo the analysis of Example 1.4, in particular recreating versions of Figures 1.3 and 1.4, for both the men and the women. Compute 90% confidence intervals for \lambda_m and \lambda_w, perhaps using different methods (arriving, in that case, to similar but not identical answers). Also, by writing

cc(\lambda) = | 1 - 2 C(\lambda) |,

get hold of the cumulative confidence distribution C(\lambda) and its derivative c(\lambda), the confidence density. Display the two c(\lambda) curves in the same diagram.

Then redo these tasks, in a Bayesian modus. Use two priors, and for these derive and display the posterior distributions for lambda, for men and for women. Compare with the confidence densitites above. The first prior takes 1/\lambda as a Gamma(a,b) with parameters (a,b) chosen to have mean 40 and standard deviation 20. The second is *your own prior*.

Then attempt to find confidence intervals and a full confidence distribution C(\rho), and the corresponding confidence curve cc(\rho), for the ratio \rho = \lambda_men/\lambda_women. Do this by working with the pivot \hat\rho/\rho.

If we have time I will also go through Exercises 2.2, 2.3, so please prepare for these too.