APMA 1660

Statistical Inference II

Spring Semester, 2012

 

Last updated May 16, 2012

 

 

 

FINAL EXAM

WEDNESDAY, MAY 16, 2PM, BH 166

 

This will be an open-book exam. No notes will be allowed. No calculators or electronic equipment of any kind will be allowed.

 

You are responsible for all the material covered in class after the midterm with the exception of the material covered in the last three classes (i.e., you are responsible for Chapters 14, 15 and 16 of the book).

 

 

EXAM

 

SOLUTIONS

 

 

 

Warm-up problems

 

SOLUTIONS

 


Useful site for conjugate priors

 

Additional information

 

·       Grades as of May 11

 

·       Additional Office Hours for week of May 7 (Daniel Johnson): Monday, Tuesday, and Wednesday 4-5 PM

 

·       Review Session on Bayesian material to be held Monday May 14th, 4–5PM, room 102A of 180 George St (not 182 George St). 

 

 

Class 23 (last)

Thursday Apr 26

 

Logistic regression.

Cross-validation.

 

Matlab code for logistic regression and cross-validation examples

 

HW6

Due Thursday, April 26

 

SOLUTIONS

 

 

Class 22

Tuesday Apr 24

 

Bootstrap.

 

Matlab code for bootstrap

 

 

Class 21

Thursday Apr 19

 

Permutation tests.

 

Matlab code for permutation test

 

 

Class 20

Tuesday Apr 17

 

Bayesian statistics continued.

 

HW5

 

Due Tuesday, April 17

 

SOLUTIONS

 

 

Class 19

Thursday Apr 12

 

The beta distribution.

Bayesian statistics. Conjugate priors.

 

 

Class 18

Tuesday Apr 10

 

Runs test and Spearman's rank correlation.

Introduction to Bayesian inference

 

 

Class 17

Thursday Apr 5

 

Kruskall-Wallis test and Friedman test.

 

 

Class 16

Thursday Apr 3

 

Rank-sum test and Mann-Whitney U test.

 

 

Class 15

Thursday Mar 22

 

Sign test and Wilcoxon signed-rank test (Chapter 15).

 

 

Class 14

Thursday Mar 20

 

Goodness-of-fit tests, continued.

 

 

Class 13

Thursday Mar 15

 

Goodness-of-fit tests (Chapter 14).

 

 

MIDTERM

Tue, March 13

 

This will be an open-book exam. No notes will be allowed. No calculators or electronic equipment of any kind will be allowed.

 

You are responsible for all the material covered in class (i.e., Chapters 11, 12 and 13), with the exception of the material covered in the last class (Geometrical interpretation of Linear Regression and ANOVA) – although it will help you with the understanding of the rest of the material.

 

Warm-up problems

 

Chapter 11:

   29, 30, 97 101, 102 (7th edition)

   25, 26, 75, 79, 80    (6th edition)

 

Chapter 13:

   26, 42, 45, 78, 85 (7th edition)

   22, 38, 39, 68, 75 (6th edition)

 

SOLUTIONS

 

Note. In the previously posted solutions, there was a mistake in 11.29 and 11.30b, where the symbol S appeared instead of S2. This has now been corrected.

 

 

EXAM

 

SOLUTIONS

 

 

Class 12

Thursday Mar 8

 

Geometrical interpretation of Linear Regression and ANOVA.

 

 

HW 4

Due Thursday Mar 8

 

6 Problems from Chapter 13 of Book:

      9, 12, 28, 66, 75, 76 (7th edition)

      7, 10, 24, 58, 65, 66 (6th edition)

 

SOLUTIONS

 

 

Class 11

Tuesday Mar 6

 

ANOVA, block design (13.8 to 13.14)

 

 

Class 10

Thursday Mar 1

 

ANOVA, one-way layout continued (13.5 to 13.7)

 

 

HW 3

Due Tuesday Feb 28

 

HW3

 

SOLUTIONS

 

Note: A good online matrix calculator can be found at

http://www.bluebit.gr/matrix-calculator/.

This calculator can be used for matrix multiplication and inversion. You can also use it to compute the Moore-Penrose inverse of matrix X (also called pseudo-inverse), equal to (X'X)–1X'. Using the Moore-Penrose inverse will simplify your calculations a bit. Make sure you use enough decimal digits in your calculations (9 should be plenty). Using any other calculation method, e.g. Matlab, is also perfectly fine.

 

 

Class 9

Tuesday Feb 28

 

ANOVA, one-way layout (13.1 to 13.4)

 

 

Class 8

Thursday Feb 23

 

Experiment design (Chapter 12)

 

 

Class 7

Thursday Feb 16

 

Multiple Linear Prediction: Inference, prediction, hypothesis tests (11.12 to 11.14)

 

 

HW 2

Due Tuesday Feb 14

 

Note: Depending on whether you use the 7th or 6th edition of the book, use the first or second set of numbers below. The two sets correspond to identical problems. If you use the 7th edition, Applet Exercises are optional.

 

Chapter 11 Problems 13, 18, 24, 26, 36, 37, 45, 51, 60 (7th edition)

Chapter 11 Problems 9,   14, 20, 22, 32, 33, 41, 45, 48 (6th edition)

 

SOLUTIONS

 

 

Class 6

Tuesday Feb 14

 

The F distribution (7.2 and 10.9)

 

Multiple Linear Regression (11.10 and 11.11)

 

 

Class 5

Thursday Feb 9

 

Simple Linear Regression: Prediction, Correlation (11.7 and 11.8)

 

Reading assignment: Section 11.9 of Book

 

 

HW 1

Due Tuesday Feb 7

 

SOLUTIONS

 

Problems 11.8, 11.11, 11.12, 11.19, 7.9, 7.10, 8.88  (7th edition)

Problems 11.4, 11.7,   11.8,   11.15, 7.1, 7.2,   8.74  (6th edition)

 

 

Class 4

Tuesday Feb 7

 

Simple Linear Regression: Inference (11.5 and 11.6)

 

 

Class 3

Thursday Feb 2

 

Chi-square and t distributions (7.2, 8.8 and 8.9) 

 

 

Class 2

Tuesday Jan 31

 

Simple Linear Regression (11.3 and 11.4) 

 

 

Class 1

Thursday Jan 26

 

Organizational matters

Examples of linear regression and ANOVA problems

Linear Statistical Models (11.1 and 11.2) 

 

 

 

Information Sheet and Syllabus

 

Instructor:     Elie Bienenstock, 182 George Street, Room 322 elie@brown.edu

                        OH: Tue 2:30-3:30, and by appointment

 

TA's:              Wei-Ying Wang

OH: Wed 2-4PM, Fri 2-3PM, 180 George St. room 102a (Computer cluster)
            Recitation: Fri 3-4PM, 180 George St. room 102a (Computer cluster)

 

Daniel Johnson

OH Tue 4-5, Thu 3-5, 182 George St. room 024

Recitation: Mon 1-2, room 205 Wilson