Statistics MS Required Courses
The four core disciplines of the Statistics M.S. program provide students the foundational structure for building their program.
Provides the framework of probability to quantify uncertainty and update beliefs given the right evidence; learn how to use a variety of strategies to calculate probabilities and expectations, both conditional and unconditional, as well as how to understand the generative stories for discrete and continuous distributions and recognize when they are appropriate for real-world scenarios.
A stochastic process is a set of random variables indexed by time or space; gain the theoretical knowledge and practical skills necessary for the analysis of stochastic systems; including basic concepts of the theory of stochastic processes and explore different types of stochastic processes including Markov chains, Poisson processes and birth-and-death processes.
Survey of regression techniques from both a theoretical and applied perspective. Numerical reasoning and predictive data modeling, with an emphasis on conceptual rather than theoretical understanding. Modeling and interpretation of observational and experimental data using linear and nonlinear regression methods. Model building and selection methods. Multivariable analysis. Fixed and random effects models. Experimental design. Practice of linear regression; Interactions and qualitative variables; analysis of variance; transformations and weighted least squares.
Statistical concepts and methods developed in a mathematical framework: Hypothesis testing, point estimation, confidence intervals. Neyman-Pearson theory, maximum likelihood estimation, likelihood ratio tests, Bayesian analysis. Asymptotic theory and simulation-based methods.
Statistics Core Courses
Students must complete all four courses to provide depth in the field of statistics. Students with prior background may replace each course with a more advanced course from the same area. All must be taken for a letter grade.
Introduction to Probability
STATS 116 Explore Courses Schedule
Textbook: A First Course in Probability, 10th ed. by Sheldon Ross
This course is a prerequisite for Introduction to Statistical Inference (Stats 200), Stochastic Process (Stats 217) and Introduction to Regression Models and Analysis of Variances (Stats 203).
Introduction to Stochastic Processes I
STATS 217 Explore Courses Schedule
- Essentials of Stochastic Processes by Durrett. Available freely here.
- An Introduction to Stochastic Modeling by Pinsky and Karlin.
- Introduction to Stochastic Processes by Ross.
- Stochastic Processes by Ross.
Introduction to Statistical Inference
STATS 200 Explore Courses Schedule
Mathematical Statistics and Data Analysis, third edition (2009) by John Rice.
Introduction to Applied Statistics
STATS 191 Explore Courses Schedule
Students with prior background may replace each course with a more advanced course from the same area:
When replacing STATS116, students must take two courses in stochastic processing or probability theory taught by the Statistics department.
- STATS 217 Intro to Stochastic Processes I *
ONE OF THE FOLLOWING
- STATS 218 Intro to Stochastic Processes II,
- STATS 219 Stochastic Processes, or
- STATS 310A Theory of Probability I
- STATS 317 Stochastic Processes
- STATS 218 Intro to Stochastic Processes II, or
- STATS 219 Stochastic Processes
- STATS 310A Theory of Probability I
*When replacing STATS 116 with 217, students do not need to replace STATS 217 - students must taken an additional course in probability or stochastic processes taught by the department when replacing STATS 116.
- STATS 300A Theory of Statistics I
- STATS 300B Theory of Statistics II
- STAT 270 A Course in Bayesian Statistics (STATS 370)
- STATS 305A Applied Statistics I
- STATS 191 Intro to Applied Statistics
At least five additional Statistics courses must be taken from graduate offerings in the department. All must be taken for a letter grade (with the exception of courses offered satisfactory/no credit only).
STATS 202 through 376A
except for the following courses that may only be used to fulfill elective credit:
Workshop in Biostatistics series STATS 260A
Independent Study (STATS 299)
Industrial Research for Statisticians (STATS 298)
Consulting Workshop (STATS 390)
Linear Algebra requirement
Students who have had linear algebra may take a more advanced mathematics course, such as from the following, or other math course with program advisor's approval. Must be taken for a letter grade.
Substitution of more advanced courses in Mathematics, that provide similar skills, may be made with consent of the advisor. All must be taken for a letter grade, with the exception of courses offered satisfactory/no credit only.
Applied Matrix Theory (Math 104)
Linear Algebra and Matrix Theory (Math 113)
Functions of a Real Variable (Math 115)
Functions of a Real Variable (Math 171)
Numerical Linear Algebra (CME 302)
Convex Optimization (CME 364A)
CS 106A/B/AX, CS 107, CS 140 - 181, or other course with the faculty advisor's approval. Students who have these skills may elect a more advanced CS course. Must be taken for a letter grade.
Substitution of other courses in Computer Science may be made with consent of the advisor. All must be taken for a letter grade, with the exception of courses offered satisfactory/no credit only.
Programming Methodology (CS 106A)
Programming Abstractions (CS 106B)
Computer Organization and Systems (CS 107)
Introduction to Scientific Computing (CME108/MATH 114)
Introduction to Scientific Computing Numerical computation for mathematical, computational, physical sciences and engineering: error analysis, floating-point arithmetic, nonlinear equations, numerical solution of systems of algebraic equations, banded matrices, least squares, unconstrained optimization, polynomial interpolation, numerical differentiation and integration, numerical solution of ordinary differential equations, truncation error, numerical stability for time dependent problems and stiffness. Implementation of numerical methods in MATLAB programming assignments. Prerequisites: CME 100, 102 or MATH 51, 52, 53; prior programming experience (MATLAB or other language at level of CS 106A or higher).
Elective courses in the area of statistics, computational mathematics and engineering, programming (Python and C/C++ programming languages), biomedical data science, economics, operations management, electrical engineering, machine learning, etc.