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STAT 632-600
October
29, 2008 Midterm Exam
Instructions: Write all your answers
on the test paper provided. Circle what you think is
the correct answer
on multiple choice
questions,
and be spectfic on short-answer
quest'ions.
Point values are indicated in parentheses.
Good luck!
1. (8) Let )/ be the set of all possible
observations.
A class
P of priors is conjugate
for a
qiven set of likelihoods
.F if
((u)J"(
.ld eP for alln
€P and all
a ey.
(b) "( .lA) e P for some n e P and all A e y.
(c) r e P implies that n('lg) is aproper
distribution
for each
A ey.
(d) the likelihood
is ploportional
to some
member of P for each
g ey.
2. (8) The Jeffreys
noninformative prior is
(a) sometimes
improper. .
(b) proportional to the squa,re
root of the determinant of the information matrix.
(pI derived from an invariance argument.
r,\
( (d) F,ll of the above.
3. (B)
An improper
prior
(a) is too subjective
for scientific
investigations.
(b) expresses
ignorance
about the underlying parameter
values.
(q) is integrable
over the parameter spape.
.t-\ " ,
/ tal Ir not necessarily
any of the
above.
\-/
4. (8) Flequentist
inferencqris
basgd on mea;ures of initial precision,
while Bayesian
inference
is baseci on measure" o; {rha/ PteetSt'o0
5. (8) Linflgy's paradox occurs when a frequentist P-value for a nullThypothesis
,F/6 is
StllA 4 and a Bayesian posterior probability for I/e is /49e
6. (B) The mean of tbe posterior distribution is often a weighted average
of what two
quantities?
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es/|hol", /
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