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.


9.40 Introduction to Neural Computation and the ability to program in MATLAB®.


Part 1: Probability Theory

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

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  

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  

Method-of-Moments Estimation

Likelihood Theory I

9 Likelihood Theory II Homework 5 due

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 will be based on problem sets, two in-class examinations and the final examination. The final grade will weight as:

Problem sets 40%
Two in-class examinations 30%
Final examination 30%