STA 215 - Problems

HW 7:
Casella & Berger Ch8, p385: 3,6 (Likelihood ratio tests)
9 (Bayes test)
14 (N-P test)
15 (definition of alpha)
20* (p-values vs. posterior prob's)
31,34 (MLR tests)
Due Sunday April 25th.
HW 6:
Casella & Berger Ch7, p331: 1,2a,6,13,20 (all about m.l.e.'s)
38 (Cramer-Rao lower bound)
41,48,55 (UMVUEs)
Due Tuesday April 20th.
NOTE
#7.2(b) requires numerical optimization. Of course feel free to do it, but it's NOT required.
#7.6(c) Please change the text of the question to: "Why can the MM not be applied here?"
HW 4/5:
GCSR Ch 5: 2,7,9,10,11
GCSR Ch 3: 6, 7, 12 (without parts b, d, e and i);
GCSR Ch 4: 1, 5.
  • For 5.7: Note that (a+b) is the "equivalent prior sample size" (i.e. plays a similar role in the prior as n in the likelihood).
  • 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 3: GCSR Ch 3: 1, 3, 4, 8.
    Solution ( postscript , pdf )
    HW 2: GCSR Ch2: 5, 9c (use Jeffreys' prior) and 2.11.
    Plus additional problems.
    Solutions:
    Chapter 2 problems (postscript)
    additional problems (postscript)
    HW 1: GCSR Ch1: 1; Ch2: 1, 2, 3a, 7ab, 9a, 10a, 12ab, 15a,20b
    Solution (ps)
    pm@stat.duke.edu