AMS 132/206: Classical and Bayesian Inference
Exam 1 solutions
1. Assume that X1 , ., Xn form a random sample from a continuous distribution with probability
density function given by
f (x | ) = x1 , for 0 < x < 1,
where > 0 is the (unknown) parameter of
University of California, Santa Cruz
Department of Applied Mathematics and Statistics
Baskin School of Engineering
AMS 132/206: Classical and Bayesian Inference (Winter 2015)
General course information
Oce
E-mail
Phone
Oce hours
Athanasios Kottas (Instruc
AMS 132: Classical and Bayesian Inference
Exam 2 solutions
1. Assume that X1 , ., Xn is a random sample from a normal distribution with unknown mean
and known variance 2 = 1. How large must the sample size n be in order for the condence interval
for , wi
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AMS 132: Classical and Bayesian Inference
Exam 2 (Thursday February 26, 2015)
This is a closed-book, closed-notes exam, with the exception of one (letter size) piece of paper with
formulas on both sides. You can use without proof any result develope
AMS 206: Classical and Bayesian Inference (Winter 2015)
Homework 1 solutions
1. Exercises 7.5.2 and 7.5.3
Solution: In exercise 7.5.2, where there is no restriction on the parameter space, the MLE for p is given
by 58/70 = 0.8286. In Exercise 7.5.3, the l
AMS 206: Classical and Bayesian Inference (Winter 2015)
Homework 2 solutions
1. Exercise 7.6.14
Solution: The rst sampling scenario species a negative binomial distribution, with parameters r and p. That is, X N B(r, p), with X representing the number of
AMS 132/206: Classical and Bayesian Inference (Winter 2015)
Data illustration of Bayesian inference
Consider the acid concentration data example discussed in Examples 8.2.3, 8.5.4 and
8.6.2 of DeGroot and Schervish (2012). The data set we work with here c
AMS 206: Classical and Bayesian Inference (Winter 2015)
Homework 3 solutions
1. Exercise 7.2.1
Solution: By denition, Pr(X6 > 3000 | x) = 3000 f (x6 | x)dx6 . We therefore require
f (x6 | x) = 0 f (x6 | )( | x)d, for which we need the posterior distributi
Name:
AMS 132/206: Classical and Bayesian Inference
Exam 1 (Thursday January 29, 2015)
This is a closed-book, closed-notes exam, with the exception of one (letter size) piece of paper with
formulas on both sides. You can use without proof any result devel
MCMC methods, with an application to Bayesian
inference for mixture distributions
Athanasios Kottas
Department of Applied Mathematics and Statistics, University of California, Santa Cruz
AMS 132/206 Classical and Bayesian Inference
March 12, 2015
Athanasi
AMS 132/206: Classical and Bayesian Inference (Winter 2015)
Simulation example: distribution of the MLE for the SD of a normal distribution
The gure on the next page includes results from a small simulation experiment to compare
the sampling distribution
AMS 206: Classical and Bayesian Inference (Winter 2015)
Homework 4 (due Thursday 3/12)
Note: All exercise numbers refer to the corresponding chapter/section from the textbook: M.H.
DeGroot and M.J. Schervish (2012), Probability and Statistics (Fourth Edit
AMS 206: Classical and Bayesian Inference (Winter 2015)
Solutions for selected homework 4 problems
1. Exercise 7.3.16
Solution: Note that, for xed mean , the standard deviation, , enters the normal likelihood
through fn (x | ) n expcfw_(0.5 n (xi )2 )/ 2