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 |
