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HW 6: GCSR Ch 5: 2,7,9,10,11

For 7: Note that (a+b) is the "equivalent prior sample size" (i.e. plays a similar role in the prior as n in the likelihood).

Solution (postscript)

HW 5: GCSR Ch 3: 6, 7, 12 (without parts b, d, e and i); Ch 4: 1, 5.

For 3.6: If necessary add an upper bound for N, say N<500. See hints for important help.

For 3.7: Add to the second part: "The outcome b has a binomial distr, with unknown probability p and sample size v+b. AND (b+v) has an indep Poisson dist with unknown mean (th_b+th_v)."

For 4.1: in part b you may use numerical optimization [for example the Splus function "nlmin"] to find the posterior mode; For part c, just write out the approximation, no need to plot the contours.

For 4.5: Remember that we showed a while ago that a rational decision maker must choose his/her decision by maximizing expected utility, i.e. as Bayes action (Loss is of course just negative utility). This exercise shows the actual form of the optial rule for three common loss (utility) functions.

Hints | Solution (postscript)

HW 4: GCSR Ch 3: 1, 3, 4, 8.

Solution (postscript)

HW 3 problems.
Due Monday, Feb 9.

Solution (postscript)

HW 2: GCSR Ch2: 5, 9c (use Jeffreys' prior) and 2.11.
Due Monday, Feb 2.

Solution (postscript)

HW 1: GCSR Ch1: 1; Ch2: 1, 2, 3a, 7ab, 9a, 10a, 12ab, 15a,20b

Solution (postscript)