Course Meeting Times
Lectures: 2 sessions / week, 1.5 hours / session
Course Description
This course is an introduction to statistics for brain and cognitive sciences. The objective of the course will be to learn to use statistical principles to evaluate, interpret and quantify uncertainty. This will provide a basis for analyzing and interpreting data from designing and conducting formal studies to reading magazine, journal and newspaper articles. The topics will be divided in three main areas: Probability theory, statistical theory and the linear model. Probability theory will cover axioms of probability, discrete and continuous probability models, law of large numbers and the Central limit theorem. Statistical theory will cover estimation, likelihood theory, Bayesian methods, bootstrap and Monte Carlo methods, hypothesis testing, confidence intervals, elementary design of experiments principles and goodness-of-fit. The linear model theory will cover the simple regression model and the analysis of variance. We will cover this technical information using examples drawn broadly from current topics in neuroscience, economics, sports and current events.
Prerequisites
9.40 Introduction to Neural Computation and the ability to program in MATLAB®.
Calendar
| LEC # | TOPICS | KEY DATES |
|---|---|---|
| Part 1: Probability Theory | ||
| 1 |
Axioms of Probability Theory, Counting Rules Conditional Probability, Bayes’ Rule and Independence |
|
| 2 | Discrete Probability Models | Homework 1 due |
| 3 | Continuous Probability Models I & II | Homework 2 due |
| 4 |
Transformations of Random Variables Joint Distributions and Independent Random Variables |
Homework 3 due |
| 5 | Conditional Distributions and Functions of Jointly Distributed Random Variables I & II | |
| In Class Examination 1 | ||
| 6 |
Expectations, Variances, Covariances and Correlation Moment Generating Functions I & II |
Homework 4 due |
| 7 | The Law of Large Numbers and the Central Limit Theorem | |
| Part 2: Statistical Theory | ||
| 8 |
Method-of-Moments Estimation Likelihood Theory I |
|
| 9 | Likelihood Theory II | Homework 5 due |
| 10 |
Propagation of Error Bootstrap and Monte Carlo Methods |
Homework 6 due |
| In Class Examination 2 | ||
| 11 | Hypothesis Testing I & II | Homework 7 due |
| Part 3: The Linear Model | ||
| 12 | Simple Regression Model I, II & III | |
| 13 | Analysis of Variance | Homework 8 due |
| Final Examination | ||
Grading
Grading will be based on problem sets, two in-class examinations and the final examination. The final grade will weight as:
| ACTIVITIES | PERCENTAGES |
|---|---|
| Problem sets | 40% |
| Two in-class examinations | 30% |
| Final examination | 30% |
