AMS207, Spring 2015, Section 01: Homework Assignments

HOMEWORK #1

Chapter 2: 8, 9, 11, 12, 13 (a) and (b), 14, 20, 21, 22. 

Chapter 3: 3, 8, 9, 11, 13

Redo the Iris Sepal example discussed in class. Explore the posterior distributions obtained under different prior scenarios.

HOMEWORK #2

Chapter 4: 1, 2, 3.

Chapter 5: 5, 7, 8, 10, 11, 13.

HOMEWORK #5

Chapter 6: 1, 2

HOWEWORK #6

Chapter 6: 6, 7

Chapter 7: 1 (only AIC and DIC), 6 (make sure you read problem 5 first). 

Compute the Gelfand & Gosh criterion in the logistic regression fit to the bioassay example of Section 3.7. Specify your loss function and the value of k that you are using. Here is the full reference:

Gelfand, A.E. and Ghosh, S.K. (1998) Model choice: A minimum posterior predictive loss approach. Biometrika, 85, 1-11.

HOMEWORK #7

Chapter 3: 5

Chapter 8: 7(a), 11 (a)-(c)

Chapter 10: 3, 5(a), (c) and (d), 8  

HOMEWORK #8

Chapter 11: 3, 4

Chapter 13: Do problem 3.12 and then do problem 2 from this chapter, 7, 9.

Consider an exponential sample that is subject to right censoring. Use the EM algorithm to find the mode of the mean of the distribution.

HOMEWORK #9

Chapter 14: 1, 3, 7, 11, 12

HOMEWORK #10

Chapter 15: 3 

Chapter 17: 1, 2, 3, 7

Consider data corresponding to a mixture of M exponential densities. Consider appropriate conjugate priors for the parameters of the model. Find the full conditionals needed to explore the posterior distribution using a Gibbs sampler.

 

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