exercises for Tue Feb 28

1. On Tue Feb 21 I rounded off Ch 2, with cross validation and other comments, before I gave a mini-version of Ch 3. I gave the BIC derivation and briefly discussed (i) Landsteiner 1924 blood groups in man and (ii) my analysis of Solzhenitsyn vs. Sholokhov. The full paper about this is here:

cas.oslo.no/getfile.php/138668/CAS_publications_events/CAS_publications/Seminar_booklets/PDF/Consilience_LidHjort.pdf

2. I also discussed the babies & mothers dataset, with model selection among 2^3 = 8 logistic regression models, etc.; see the R script com12b.

3. For Tue Feb 28 do the following.

(i) Make sure you understand and can use com12b and moficiations. Check what happens with a different mother than Mrs Jones (create her yourself). Supplement the AIC analysis with AIC^*, for which you need \hat p^* = Tr(\hat J^{-1} \hat K) for each of the 8 models. Derive the relevant formulae for \hat J and \hat K (see Ch 2), and find the \hat p^* numbers.

(ii) Apply your knowledge & versatility to do the first half of Exercise 20 in the Nils collection, about Poisson regression for the number of bird species on islands outside Ecuador. Do AIC, BIC, AIC^*, again needing \hat J and \hat K. You might try to start with com12b and modify parts accordingly, from logistic regression to Poisson regression.

(iii) For both of (i) and (ii), supplement your analyses and model selections with cross validation.

4. On Tue Feb 28 I will say something more on the BIC, and probably take us through section 4.1-4.2. After that we start with "the 2nd half of the course", namely Chs 5-6-7.