Exercises for Mon 2 May

1. On Mon 25 April we went through various exercises from Chs 7 and 8, with appropriate semidigressions to maximum simulated likelihood, Gibbs models, tilting of parametric start models, etc. I also went through some aspects of Ch 11, and will go on the confidence curves for quantiles next week.

2. We've agreed (some time ago, but not written it here) that *the Exam Project* will be made available Wed June 1, with written reports to be handed in Mon June 13. The four-hour written exam will be held Thu June 16.

3. Exercises for Mon 2 May: First, do exercise 7.5, for an imagined data set of (x_i,y_i) from the binormal with means zero and variances one, for which U_n = the avarge of (x_iy_i) = 0.666 and V_n = the average of (x_i^2 + y_i^2) = 1.888. Check that the ML estimate is 0.719. For a few values of n, construct as many as four CDs, with associated confidence curves, and compare them: (1) the 1st order large-sample normal approximation one; (2) C^*(\rho) = Pr_\rho [ \hat\rho > \hat\rho_\obs ]; (3) based on t-bootstrapping; (4) based on Bartletting the deviance and the chi-sqared(1). Second, do exercise 8.14, with the modification that the function used in the exponential tilting of the Poisson is T(y) = \sqrt{y+1}. Carry out ML analysis and give the approximate cc(\gamma). Also compute the optimal cc for \gamma. This necessitates sampling from a certain distribution for \sum T(y_i), given \sum y_i = 48, for each value of \gamma. Try to do this via MCMC.