**Lectures:** Tuesday, 4:30-7:10pm, Robinson Hall, room B203

Some of the lectures will be based on the instructor's notes posted on this website. The lectures themselves will not be posted. Some lectures will be accompanied only by notes written on the board.

Be sure to get the corrections at the author's website

A useful supplement is Jun Shao (2005),

I plan to cover most of the material in the first four chapters in Shao during 972 in the fall semester, and I plan to cover the most of the remainder in 973.

At the level of this course, no single text can cover "everything". The student is encouraged to study other texts on the various topics; see, for example, the references listed in the general description of the course.

My evolving Companion notes may also be useful. These notes, which include an index and a bibliography, are not complete, and are not meant to be. Their purpose is to provide a few additional examples, and some more detailed discussion of some things. I will add to them frequently, so I do not recommend printing them.

One learns mathematical theory primarily by individual work; that is, by supplying the successive steps in solving a problem or proving a theorem. Some mathematical theory is learned and reinforced by passive activities such as reading or listening to lectures and discussions, and the assigned readings and weekly lectures are meant to serve this purpose. The reading assignments listed in the schedule below should be carried out with a pencil and paper in hand. The readings should be iterated as necessary to achieve a complete understanding of the material.

The primary means of communication outside of class will be by email.

Students must use their Mason email accounts to receive important University information, including messages related to this class. (You may, of course, foward email from your Mason email account to one that you check regularly.)

If you send email to the instructor, please put "CSI 972" or "STAT 972" in the subject line.

Student work in the course (and the relative weighting of this work in the overall grade) will consist of

For in-class exams, one sheet of notes will be allowed. The preparation of that sheet is one of the most important learning activities.

The problems do not need to be worked sequentially (some are much harder than others); when you are stuck on one problem, go on to the next one.

Students are not to communicate concerning exams with each other or with any person other than
the instructor. On take-home exams, any **passive ** reference
is permissible (that is, the student
cannot ask someone for information, but the student may use any existing information from
whatever source).

Students are expected to read the relevant material in the text prior to each class (after the first one).

Students are strongly encouraged to solve the "exercises for practice and discussion", especially those marked with an asterisk.

How to learn mathematical statistics (working problems and remembering the big picture); "easy pieces".

Fundamentals of measure theory: sigma-fields, measures, integration and differentiation.

In Companion, Exercises 0.0.14, 0.1.1, 0.1.4, 0.1.8, 0.1.10, 0.1.13, 0.1.25.

In Companion, Exercises 1.8, 1.12, 1.24, 1.29, 1.39, 1.46, 1.56(a).

In Companion, Exercises 1.67, 1.69, 1.73, 1.74

Basic statistical concepts: Sufficiency and completeness.

**Reading assignments:**
Companion notes, Chapter 2, and
Shao, Chapter 2.

**Exercises for practice and discussion:** In Shao Exercises 2.6: problems
9, 13, 19, 23, 25, 30, 44, 56, 66, 74, 84, 93, 101, 115, 121.

**Assignment 4, due September 27:**
In Shao Exercises 2.6: problems 3, 5, 7, 20, 27.

Due October 18

Between now and the end of class on October 18, students are not to discuss homework or other aspects of the course (including the takehome of course!) with anyone other than the instructor.

Review inclass exam.

Decision theory.

Decision theory and general review of Shao Chapter 2.

Bayesian inference

**Reading assignment:**
Companion notes, Chapter 3.

**Assignment 6, due November 1:**
In Shao problems 4.1(a)(b), 4.17, 4.18, 4.31, 4.32(a), 4.38(a)(b).

U statistics.

Linear models.

Finite population sampling.

Asymptotically unbiased estimators.

Closed book and closed notes except for one sheet of prewritten notes.