9.07 Statistics for Brain and Cognitive Sciences Prereq: 18.01 and 18.02 or permission of instructor (Spring) 3-0-9 This course is an introduction to statistical theory for brain and cognitive sciences. 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. E. Brown Lectures Probability Theory September 5: Introduction: Course Overview Lecture 1 Axioms of Probability Theory, Counting Rules Rice, p.1-13 September 10: Lecture 1 Conditional Probability, Bayes’ Rule and Independence Rice, p. 16-26. September 12: Lecture 2 Discrete Probability Models (Homework 1 due) Rice, p.35-40, 42-47, 116-118, 130-133 September 17: Lecture 3 Continuous Probability Models Rice p. 47-64, 118-120, 130-133 September 19: Lecture 3 Continuous Probability Models (Homework 2 due) Rice p. 47-64, 118-120, 130-133 September 24: Student Holiday September 26: Lecture 4 Transformations of Random Variables Rice p. 58-64 October 1: Lecture 4 Joint Distributions and Independent Random Variables (Homework 3 due) Rice p. 71-86 October 3: In Class Examination 1 October 10: Lecture 5 Conditional Distributions and Functions of Jointly Distributed Random Variables Rice p. 87-104, 121-132 October 15: Lecture 5 Conditional Distributions and Functions of Jointly Distributed Random Variables Rice p. 87-104, 121-132 October 17: Lecture 6 Expectations, Variances, Covariances, Correlation and Moment Generating Functions Rice p. 138-148, 155-161 (Homework 4 due)page 2: Syllabus 9.07 Statistics Brain and Cognitive Sciences October 22: Lecture 6 Expectations, Variances, Covariances, Correlation and Moment Generating Functions, Rice p. 138-148, 155-161 October 24: Lecture 7 The Law of Large Numbers and the Central Limit Theorem (Homework 5 due) Rice, p. 177-188 Statistical Theory October 29: Lecture 8 Method-of-Moments Estimation Rice, p. 257-265 October 31: Lecture 9 Likelihood Theory Rice, p. 267-279 November 5: In Class Examination 2 November 7: Lecture 9 Likelihood Theory (Homework 6 due) Rice, p. 267-279 November 14: Lecture 11 Propagation of Error, Bootstrap and Monte Carlo Methods Rice, p. 260-266, 284-285, 311-312, 399-401 November 19: Lecture 11 Propagation of Error, Bootstrap and Monte Carlo Methods Rice, p. 260-266, 284-285, 311-312, 399-401 November 21: Lecture 10 Bayesian Methods I (Homework 7 due) Rice, p. 285-297 November 26: Lecture 10 Bayesian Methods II Rice, p. 285-297 November 28: Lecture 12 Hypothesis Testing I (Homework 8 due) Rice, p. 329-337, 420-451 December 3: Lecture 12 Hypothesis Testing II Rice, p. 420-451 The Linear Model December 5: Lecture 14 Simple Regression Model I Rice p. 542-563 December 10: Lecture 14 Simple Regression Model II (Homework 9 due) Rice p. 542-563 December 12: Lecture 16 Analysis of Variance Rice p. 477-505 December 19: Final Examination (9:00-12:00, 46-3310) Problem Sets (approximately every week to ten days)page 3: Syllabus 9.07 Statistics Brain and Cognitive Sciences Problems Sets will be due at 5 p.m. on the day indicated. Everyone will be allowed to drop the score on one problem set in computing the final grade. Grading Grading will be based on the 9 problem sets, two in-class examinations and the final examination. The final grade will weight the problem set 40%, the two in-class examinations (30%) and the final examination (30%). Lecture Notes The primary course material will be the lecture notes posted on the course web page for each lecture. Course Textbook Rice, JA, Mathematical Statistics and Data Analysis, 3rd edition. Boston, MA Other Text References Dekking, F.M., Kraaikamp, C. Lopuhaa, Meester, L.E. A Modern Introduction to Probability and Statistics. London: Springer-Verlag, 2002. DeGroot MH, Schervish MJ. Probability and Statistics, 3rd edition. Boston, MA: Addison Wesley, 2002. Rosner B. Fundamentals of Biostatistics, 6th edition. Boston, MA: Duxbury Press, 2006. Pawitan Y. In All Likelihood: Statistical Modeling and Inference Using Likelihood. London: Oxford,