S620: Introduction To Statistical Theory
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.
Year(s) Offered: _2018
Class time: Monday, Wednesday : 1:00PM - 2:15PM
Website: To be constructed.
Instructor: Jaime Ramos
Other Contact(s): Jaime Ramos - email@example.com
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.
Exams: Two midterms and a final exam.
Keywords: Mathematical statistics. Statistical Inference theory. Maximum likelihood estimation. Sufficiency. Bayesian ideas. Decision theory.