Mathematical Statistics-E2

Numbering Code U-LAS11 10010 LE55 Year/Term 2021 ・ First semester
Number of Credits 2 Course Type Lecture
Target Year Mainly 2nd year students Target Student For science students
Language English Day/Period Thu.3
Instructor name Croydon, David Alexander (Research Institute for Mathematical Sciences Associate Professor)
Outline and Purpose of the Course This course will develop the theory of statistical inference, which has applications across the natural and social sciences, and beyond. It will focus on the key topics of parameter estimation and hypothesis testing. As well as presenting the theoretical justification for various techniques covered, it will also be a goal to show how these can be applied in examples.
Course Goals - To understand the basic concepts of, and mathematical justification for, point estimation and hypothesis testing
- To be able to apply key techniques of statistical inference in applications
Schedule and Contents The following indicates possible topics that will be covered and approximate schedule, though the precise details may vary depending on the student's proficiency level and background.

(1) Review of probability theory [2 weeks]
Distribution and expectation, multivariate distributions, conditional distributions, notions of convergence, common families of distributions, random samples

(2) Point estimates [5 weeks]
Estimators, sampling distribution, parameterized statistical models, maximum likelihood estimates, sampling distributions, confidence intervals, point estimation for linear models

(3) Hypothesis testing [5 weeks]
Likelihood ratio tests, methods of evaluating tests, goodness of fit tests, tests for comparing mean and variance of two samples, tests for independence

(4) Applications [2 weeks]
Extended example applications of the main techniques covered earlier in the course

Total: 14 classes and 1 week for feedback
Evaluation Methods and Policy There will be regular exercise sheets throughout the course, for which students will be expected to return work and present some of their answers in class. This will account for 70% of the final mark. The remaining 30% will be based on a final exam.

NB. In case a final exam is not possible, the written assignments will account for 100% of the final mark.
Course Requirements No statistical knowledge will be assumed. However, some basic calculus (e.g. finding the maximum of a function using differentiation) will be helpful.
Study outside of Class (preparation and review) The lecturer will present the basic concepts in class, upon which assignments will be set. The time for these might vary from week to week, and student to student, but the lecturer estimates these to take 1-2 hours
Textbooks Textbooks/References There will be no set textbook for the course, as the lectures will contain all the material needed for the homework and exam. However, students might find the following useful as additional reading:

Statistical Inference, Casella and Berger, Duxbury, 2002