# Statistics MS Required Courses (2023-24)

The four core disciplines of the Statistics M.S. program provide students the foundational structure for building their program.

**Probability Theory**

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.

**Stochastic Processes**

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.

**Applied Statistics**

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 Theory**

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

**Prerequisites:**

**MATH 52**

**and familiarity with infinite series, or equivalent. Please note that students must enroll in one section in addition to the main lecture.**

**Note: Students who have not had prior Probability coursework may consider taking the prerequisite prior to starting the program.**

**Terms: Aut, Spr, Sum | Units: 4**

**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).

As stated in the Stanford bulletin, enrollment in STATS 116 after successfully completing STATS 217, 218, and/or 219 may not be used to fulfill degree requirements, including as an elective.”

##
Introduction to Stochastic Processes I

STATS 217 Explore Courses Schedule

**Prerequisite: a post-calculus introductory probability course e.g.**

**STATS 116**

**Terms: Win | Units: 3**

**Useful Textbooks:**

*Essentials of Stochastic Processes*by Durrett*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

**Prerequisite:**

**STATS 116**

**. Please note that students must enroll in one section in addition to the main lecture.**

**Note: Students who have not had prior Probability coursework may consider taking the prerequisite prior to starting the program. Otherwise, students should take STATS116 autumn quarter followed by STATS200 in winter quarter.**

**Terms: Aut, Win | Units: 4**

**Textbook:**

Mathematical Statistics and Data Analysis, third edition (2009) by John Rice.

##
Introduction to Applied Statistics

STATS 191 Explore Courses Schedule

**Prerequisite: introductory statistical methods course.**

**Recommended: 60, 110, or 141.**

**Terms: Win | Units: 3**

Students with prior background may replace each course with a more advanced course from the same area:

##
STATS 116

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
- When replacing STATS 116 with 217, students do not need to replace STATS 217 however, students must take an additional course in probability or stochastic processes taught by the department when replacing STATS 116.

* and/or* 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 221 Random Processes on Graphs and Lattices

##
STATS 217

When replacing STATS 217, students must take either

- STATS 218 Intro to Stochastic Processes II, or
- STATS 219 Stochastic Processes
- STATS 310A Theory of Probability I

##
STATS 200

When replacing STATS 200, students may take either:

- STATS 300A Theory of Statistics I
- STATS 300B Theory of Statistics II
- STAT 270 A Course in Bayesian Statistics (STATS 370)

##
STATS 191

In this order, students may replace:

- STATS 191

or

- STATS 203 Introduction to Regression Models and Analysis of Variance

or

- STATS 305A Applied Statistics I

### Statistics Depth

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:

##
NeuroTech Training Seminar (STATS 242)

**Terms: Aut, Wtr, Spr | Units: 1-2 | Repeatable for credit**

##
Workshop in Biostatistics series (STATS 260)

**Terms: Aut, Wtr, Spr | Units: 1-2 | Repeatable for credit**

##
Topics in Computing for Data Science (STATS/BIODS 352)

**Terms: Aut | Units: 1**

##
Industrial Research for Statisticians (STATS 298)

**Terms: Aut, Win, Spr, Sum | Units: 1-5 | Repeatable for credit**

**Full-time work in summer only.**

##
Independent Study (STATS 299)

**Terms: Aut, Win, Spr, Sum | Units: 1-5 | Repeatable for credit**

##
Literature of Statistics (STATS 319)

Literature study of topics in statistics and probability culminating in oral and written reports.

**Terms: Aut, Win, Spr, Sum | Units: 1 | Repeatable for credit**

##
Consulting Workshop (STATS 390)

**Prerequisites: course work in applied statistics or data analysis, and consent of instructor.**

**Terms: Aut, Win, Spr, Sum | Units: 1 | Repeatable for credit**

### 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.

### Select one of the following:

##
Applied Matrix Theory (Math 104)

**Terms: Aut, Win, Spr | Units: 3**

##
Linear Algebra and Matrix Theory (Math 113)

**Prerequisites:**

**Math 51**

**Terms: Aut, Win, Spr | Units: 3**

##
Functions of a Real Variable (Math 115)

**Prerequisite: 21.**

**Terms: Aut, Spr | Units: 3**

##
Functions of a Real Variable (Math 171)

offered A,S,Su

##
Numerical Linear Algebra (CME 302)

offered A

##
Convex Optimization (CME 364A)

offered W

### Programming requirement

CS 106A/B, CS 107, CS 140 - 182, 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)

offered A,W,S,Su

##
Programming Abstractions (CS 106B)

offered A,W,S,Su

##
Computer Organization and Systems (CS 107)

offered A,W,S

##
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).

**offered W,Su**

### Breadth/General Electives

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.

Up to 6 units of the following courses may be used to fulfill breadth/elective credit:

- STATS 260 series: Workshop in Biostatistics (1-2 units)
- STATS 242: NeuroTech Training Seminar (1 unit)
- STATS 352: Topics in Computing for Data Science (1 unit)
- STATS 298/398: Industrial research of statisticians (1 unit)
- STATS 299/399: Independent study/research (1 unit)
- STATS 319: Literature of Statistics (1 unit)
- STATS 390: Statistical Consulting (1 unit)