Syllabus

Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

Prerequisites

Probability and Random Variables (18.440) or Probabilistic Systems Analysis (6.041)

Topics

Maximum Likelihood Estimators

  • Properties
  • Fisher Information
  • Asymptotic Variance of MLE

Parameters of Normal Distribution

  • Chi-squared and t-Distribution
  • Distribution of the Estimates of Parameters of Normal Distribution
  • Confidence Intervals

Testing Hypotheses

  • t-Tests and F-Tests
  • Bayes Tests
  • Most Powerful Tests (Including Randomized)

Goodness-of-fit Tests

  • Simple Discrete
  • Continuous
  • Composite Goodness-of-fit Tests
  • Independence and Homogeneity Tests
  • Kolmogorov-Smirnov Test

Linear Regression

  • Estimating Parameters
  • Joint Distribution of Estimates
  • Testing Hypotheses about Parameters
  • Confidence and Prediction Intervals
  • Joint Confidence Sets

Multiple Regression, Analyses of Variance and Covariance

  • Distribution of Estimates
  • Testing General Linear Hypotheses

Grading

ACTIVITIES weightS
Ten Problem Sets 10 points each
Two Midterm Exams 150 points each

Text

DeGroot, Morris H., and Mark J. Schervish. Probability and Statistics. 3rd ed. Boston, MA: Addison-Wesley, 2002.

Calendar

The calendar below provides information on the course’s lecture (L) and exam (E) sessions.

SES # TOPICS KEY DATES
L1 Overview of some Probability Distributions  
L2 Maximum Likelihood Estimators  
L3 Properties of Maximum Likelihood Estimators Problem set 1 due
L4 Multivariate Normal Distribution and CLT  
L5 Confidence Intervals for Parameters of Normal Distribution Problem set 2 due
L6 Gamma, Chi-squared, Student T and Fisher F Distributions Problem set 3 due
L7-L8 Testing Hypotheses about Parameters of Normal Distribution, t-Tests and F-Tests Problem set 4 due in Ses #L8
L9

Testing Simple Hypotheses

Bayes Decision Rules

Problem set 5 due
E1 Exam 1  
L10 Most Powerful Test for Two Simple Hypotheses  
L11 Chi-squared Goodness-of-fit Test  
L12 Chi-squared Goodness-of-fit Test for Composite Hypotheses  
L13 Tests of Independence and Homogeneity Problem set 6 due
L14 Kolmogorov-Smirnov Test  
L15-L16 Simple Linear Regression Problem set 7 due
L17-L18 Multiple Linear Regression Problem set 8 due
L19-L20

General Linear Constraints in Multiple Linear Regression

Analysis of Variance and Covariance

Problem set 9 due

Problem set 10 due in Ses #L20

E2 Exam 2  
L21 Classification Problem, AdaBoost Algorithm  
L22 Review  

Course Info

Learning Resource Types

grading Exams
notes Lecture Notes
assignment Problem Sets