M378K: INTRODUCTION TO MATHEMATICAL Fall 2014 Instructor: Dr Stephen Walker ([email protected])

10.174 RLM Lectures: Monday & Wednesday & Friday, 11.00 to 12.00.

Office hours: Monday and Wednesday, 9.00 to 10.30

Textbooks: Schaums's Outline of Statistics, Fourth Edition (Schaums's Outline Series). Murray Spiegel and Larry J. Stephens. Introduction to , Fifth Edition (Wiley Series in & Mathematical Statistics). Paul G. Hoel. Content: The course will be developed from the notion that Statistics is about performing operations on variables arising from distribution functions. The specific operations involve implementing tasks such as estimation, both and , and hypothesis testing. Many of the concepts will be demonstrated on the normal distribution and more broadly the where properties of the procedures will be derived. Throughout, emphasis will be placed on the understanding of what the statistical goals are. Specific topics covered in some depth include hypothesis testing (e.g. likelihood ratio tests, most powerful tests); asymptotic analysis (the pinning down of procedures when sample sizes are large); nonparametric methods (no distributional assumptions are made in the quest for summaries); notions of sufficiency, multivariate analysis and a brief flirtation with Bayesian statistics. Prerequisites: Mathematics 362K. Class Notes: Notes for the lectures will provided on Canvas at the start of each week. Exams: There will be 2 exams; set approximately at 1/3 and 2/3 of the way during the course, and will be set during regular class, and the final exam. Assignments: A number of assignments will be set during the course. Grades: Grades for the course will be allocated as follows: 80% for the Exams and 20% for the Assignments. Tentative Schedule: Week Topic 1. Introduction to Statistics 2. The normal distribution and point estimation 3. The normal distribution, confidence intervals and hypothesis testing 4. Two sample tests (+Assignment 1) 5. The exponential family 6. Sufficiency (+Exam 1) 7. Linear models 8. Nonparametric methods (+Assignment 2) 9. 10. Asymptotics 11. More on hypothesis testing (+Exam 2) 11. Bayesian methods 12. Sample size selection (+Assignment 3) 13. Method of moments 14. Estimation methods, e.g. EM algorithm (+Assignment 4) 15. Summary

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