# 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

Probability spaces as models for phenomena with statistical regularity. Discrete spaces (binomial, hypergeometric, Poisson). Continuous spaces (normal, exponential) and densities. Random variables, expectation, independence, conditional probability. Introduction to the laws of large numbers and central limit theorem.

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

Discrete and continuous time Markov chains, Poisson processes, random walks, branching processes, first passage times, recurrence and transience, stationary distributions. Non-Statistics masters students may want to consider taking STATS 215 instead.

This course is the first of a two-quarter sequence (along with STATS 218) exploring the rich theory of stochastic processes and some of its many applications. The main topics covered this quarter are random walks, Poisson processes, discrete and continuous time Markov chains, and branching processes.

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

Modern statistical concepts and procedures derived from a mathematical framework. Statistical inference, decision theory; point and interval estimation, tests of hypotheses; Neyman-Pearson theory. Bayesian analysis; maximum likelihood, large sample theory.

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

Statistical tools for modern data analysis. Topics include regression and prediction, elements of the analysis of variance, bootstrap, and cross-validation. Emphasis is on conceptual rather than theoretical understanding. Applications to social/biological sciences. Student assignments/projects require use of the software package R.

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)
This is a required course for students in the NeuroTech training program, and is also open to other graduate students interested in learning the skills necessary for neurotechnology careers in academia or industry. Over the academic year, topics will include: emerging research in neurotechnology, communication skills, team science, leadership and management, intellectual property, entrepreneurship and more.

Terms: Aut, Wtr, Spr | Units: 1-2 | Repeatable for credit
Workshop in Biostatistics series (STATS 260)
Applications of statistical techniques to current problems in medical science. To receive credit for one or two units, a student must attend every workshop. To receive two units, in addition to attending every workshop, the student is required to write an acceptable one page summary of two of the workshops, with choices made by the student.

Terms: Aut, Wtr, Spr | Units: 1-2 | Repeatable for credit
Topics in Computing for Data Science (STATS/BIODS 352)
A seminar-style course jointly supported by the Statistics department and Stanford Data Science, and suitable for doctoral students engaged in either research on data science techniques (statistical or computational, for example) or research in scientific fields relying on advanced data science to achieve its goals. Seminars will usually consist of a student presentation of a relevant technical topic followed by discussion of the topic by all. Topics will be assigned to individuals to combine relevance for the course and suitability to the individual student's background and research interests. Prerequisites: Competence in the basic data science needed for the student's research goals plus preparation for presenting a suitable topic. Before enrolling, participants should have a topic approved as prescribed on the STATS352 website.

Terms: Aut | Units: 1
Industrial Research for Statisticians (STATS 298)
Masters-level research as in 299, but with the approval and supervision of a faculty adviser, it must be conducted for an off-campus employer. Students must submit a written final report upon completion of the internship in order to receive credit. Repeatable for credit. Prerequisite: enrollment in Statistics M.S. program.

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

Full-time work in summer only.
Independent Study (STATS 299)
For Statistics M.S. students only. Reading or research program under the supervision of a Statistics faculty member. May be repeated for credit.

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)
Skills required of practicing statistical consultants, including exposure to statistical applications. Students participate as consultants in the department's drop-in consulting service, analyze client data, and prepare formal written reports. Seminar provides supervised experience in short term consulting. May be repeated for credit.

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)
Linear algebra for applications in science and engineering: orthogonality, projections, spectral theory for symmetric matrices, the singular value decomposition, the QR decomposition, least-squares, the condition number of a matrix, algorithms for solving linear systems. MATH 113 offers a more theoretical treatment of linear algebra. MATH 104 and ENGR 108 cover complementary topics in applied linear algebra. The focus of MATH 104 is on algorithms and concepts; the focus of ENGR 108 is on a few linear algebra concepts, and many applications.

Prerequisites: MATH 51 and programming experience on par with CS 106.

Terms: Aut, Win, Spr | Units: 3
Linear Algebra and Matrix Theory (Math 113)
Algebraic properties of matrices and their interpretation in geometric terms. The relationship between the algebraic and geometric points of view and matters fundamental to the study and solution of linear equations. Topics: linear equations, vector spaces, linear dependence, bases and coordinate systems; linear transformations and matrices; similarity; eigenvectors and eigenvalues; diagonalization. Includes an introduction to proof-writing.

Math 104 offers a more application-oriented treatment.

Prerequisites: Math 51

Terms: Aut, Win, Spr | Units: 3
Functions of a Real Variable (Math 115)
The development of real analysis in Euclidean space: sequences and series, limits, continuous functions, derivatives, integrals. Basic point set topology. Includes introduction to proof-writing.

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

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)