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
Grading criteria.
| 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. ISBN: 0201524880.
Calendar
The calendar below provides information on the course's lecture (L) and exam (E) sessions.
Course calendar.
| 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 |
|