## S620: Introduction To Statistical Theory

### Class Description

Fundamental concepts and principles of data reduction and statistical inference, including the method of maximum likelihood, the method of least squares, and Bayesian inference. Theoretical justification of statistical procedures introduced in S320.

### Class Information

**Semester(s): **Spring

**Semester(s) Offered: ** Spring

**Class time: **
Tuesday, Thursday

**Website: **To be constructed.

**Capacity: ** Combined enrollment for Spring 2012 was 20 students.

### Contact Information

**Instructor: **Andrew Womack - ajwomack@indiana.edu

**Other Contact(s): ** Andrew Womack - ajwomack@indiana.edu

### Other Details

**Sequence: ** Not part of a sequence

**Prerequisites: ** STAT S-320/520 (Introduction to Statistics) and MATH M-463 (Introduction of Probability Theory I).

**Algebra Required?: ** Not extensive. Used for basic matrix representations. Not much in homeworks or proofs.

**Calculus Required?: ** Some knowledge of integration and differentiation is needed. Understanding of probability distributions and some basic knowledge of expectations and variances is needed along with parametric representations of distributions.

**Day(s) per week offered: ** Historically it has been taught TR in 75-minute class meetings. It can be taught in the MWF format. No computer Lab.

**Recommended follow-up classes: ** This course allows students to take other classes that require some degree of knowledge in statistical inference. Examples are: S-625 Nonparametric Statistics and S-626 Bayesian Theory and Data Analysis.

**Substantive Orientation: ** Designed for students in graduate degree programs in the Department of Statistics

**Books used: ** DeGroot and Schervish, Probability and Statistics, 4th Edition (2011)

**Applied/Theoretical: ** This is mainly a theory course. Some data examples are considered.

**Software Used: **
R

**How the software is used: ** Graphs of distributions. Calculations of probabilities and quantiles. Basic Monte Carlo random number simulations.

**Problem Sets: ** Yes

**Data Analysis: ** Basic data examples.

**Presentations: ** No

**Exams: ** Two midterms and a final exam.

**Keywords: ** Mathematical statistics. Statistical Inference theory. Maximum likelihood estimation. Sufficiency. Bayesian ideas. Decision theory.

**Comments: ** S620 meets concurrently with S420, a required course for undergraduate statistics majors.