6.434J/16.391J Statistics for Engineers and Scientists --- Spring 2006

Time and Place

Tuesday and Thursday, 1:00pm - 2:30pm, Room 56-154

Instructor

Prof. Moe Z. Win, moewin@mit.edu, Room 32-D658, (617) 253-9341
Office hours:  Tuesday, 2:30pm - 3:30pm, Room 32-D658

Guest Lecturers

Dr. Henk Wymeersch, hwymeers@mit.edu, Room  32-D782

TA

Faisal M. Kashif, fmkashif@mit.edu, Room 32-D674A, (617) 324-0175
Office hours:  Wednesday, 2:00pm – 3:00pm, Room 32-D674A (or 6th Floor Lounge)

Reference Textbooks

 

1.      Edward J. Dudewicz and Satya N. Mishra, Modern Mathematical Statistics, New York: John Wiley & Sons, 1988. [ Requested]

2.      Harry L. Van Trees,  Detection, Estimation, and Modulation Theory, Part I. Detection, Estimation, and Linear Modulation Theory, New York: John Wiley & Sons, 2001.

3.      Robert V. Hogg and Allen T. Craig, Introduction to Mathematical Statistics, Upper Saddle River, NJ: Prentice Hall, 1995.

4.      Peter J. Bickel and Kjell A. Doksum, Mathematical Statistics: Basic Ideas and Selected Topics, Vol I, Upper Saddle River, NJ: Prentice Hall, 2001. [Call number  QA276.B47 2001]

5.      John A. Rice, Mathematical Statistics and Data Analysis, Belmont, CA: Duxbury Press, 1995.  [Call number QA276.12.R53 1995 ]

Reference textbooks will be available in the reserve section of Barker library (10-500).

Handouts and Lecture Notes

 

Exams

 

Problem Sets and Project

 

 

Due date

 

Problem Set 1; Solutions1

Feb 16

Problem Set 2; Solutions2

Feb 28

Problem Set 3; hw3dataset.m; Solutions3

Mar 9

Problem Set 4; Solutions4

Mar 16

Project; Test Data1; TestData2;

Apr 20

Problem Set 5; Solutions5

Apr 11

Problem Set 6; Solutions6

Apr 25

Problem Set 7; hw7p2.mat; Solutions7

May 4

Problem Set 8; Solutions8

Never

 

 

Lectures

 

 

Date

Topics

Handouts

 

1.

Tue, Feb 7

Review of Probability, Motivation for studying statistics

 

2.

Thu, Feb 9

Some useful distributions, some important relations

Syllabus, PS1

3.

Tue, Feb 14

Definition of statistic, Introduction to Estimation/Detection Theory (EDT), Cost Function, Bias, Variance and Biased Estimators

 

4.

Thu, Feb 16

Biased and Unbiased Estimators, ML Estimators

 

5

Thu, Feb 23

Non-diff’ble cases for ML estimation, Multiple parameter estimation; examples

 

6

Tue, Feb 28

Types of estimators. MMSE and LMMSE

 

7

Thu, Mar 2

 Non-Bayesian Estimators: ML, BLU, LS. Relationships between estimators, examples.

 

8

Tue, Mar 7

Fisher’s  Information Inequality (Cramer-Rao Bound)

 

9

Thu, Mar 9

CRLB / Information Inequality, Sufficient Statistics

 

10

Tue, Mar 14

Sufficient Statistics, Neyman Factorization Theorem

 

11

Thu, Mar 16

Exponential Families, Minimal Sufficient Statistics

 

12

Tue, Mar 21

Minimal Sufficient Statistics, Minimality and Exp. Family, Rao-Blackwell Theorem

 

13

Thu, Mar 23

Exam 1

 

14

Tue, Apr 4

Hypothesis Testing, LRT

 

15

Thu, Apr 6

Examples, ROC, Probability of error, Q function

 

16

Tue, Apr 11

Bayesian Hypothesis Testing, Neyman Pearson Test, ROC, Discrete-valued variables

 

17

Thu, Apr 13

multiple hypothesis testing, composite hypothesis testing, examples

 

18

Thu, Apr 20

Generating random variables, Monte Carlo (MC) methods, importance/weighted importance sampling, examples

 

19

Tue, Apr 25

The EM Algorithm

 

20

Thu, Apr 27

Mixture Density and EM algorithm

 

21

Tue, May 2

Confidence Intervals

 

22

Thu, May 4

Factor Graphs and Sum-Product Algorithm, Solving inference problems with FG

 

23

Tue, May 9

Factor Graphs contd.. Kalman Filter example.

 

24

Thu, May 11

Introduction to Wireless Communications, Background for Random Matrix Theory

 

25

Tue, May 16

Introduction to Random Matrix Theory; exam review

 

26

Wed, May 17

Exam 2