Exercises for Wed Feb 20

1. On Wed Feb 13 I rounded off Ch 2 and did the essential BIC approximation thing for Ch 3. We did J and K analysis for the normal, learning both about normal approximations and about which standard results for the normal that cannot be trusted if the model is not correct. I also spent time doing extra exercises (a) KL(g, f_\theta) for given g, with various illustrations, and (b) modelling football results, via (y1, y2, fifa1, fifa2). For these, check com15b and the file football_data on the course site.

2. Next week I more or less round off Ch 3.

3. Exercises for Wed Feb 20 are as follows.

(a) Find the Exam Project 2017 and do Exercise 1.

(b) Work with the 254 football matches, with data to be organised into (y1, y2, fifa1, fifa2) (with data collected and organised by Nils in 2007). Try out some models, and don't give up until you have something working better, in terms of AIC, than the already satisfactory model which takes independent Poisson with rates \lambda_0 \exp(\beta r), where r is fifaown/fifacompetitor.

(c) You observe two binomials, y1 = 28 from bin(50, p1) and y2 = 22 from bin(50, p2). Work through AIC and BIC inferences for ModelA, which takes p1 = p2, and ModelB, which takes p1 and p2 different. Do also exact Bayesian calculations for Pr(ModelA | data) and Pr(ModelB | data), where the two models have equal prior probabilities 0.50, where the common p is uniform(0,1) for ModelA, and where the p1 and p2 are independent and uniform(0,1) for Model B.