# Statistics MS Required Courses (2024-2025)

Prerequisites:

- Multivariable calculus (differential and integral) and linear algebra at the level of MATH 51 & 52
- Introductory programming at the level of CS 106A
- Intermediate statistics (multiple regression and ANOVA, possibly without linear algebra) at the level of STATS 191
- Introductory probability at the level of STATS 117

These courses cannot be counted toward the 45 units required for the M.S. degree.

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 - 4 courses

(12-14 units) Must be taken for a letter grade.

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.

- STATS 118: Probability Theory for Statistical Inference (4 units)
- Advanced students may replace with STATS 218 or 310A.

- STATS 200: Introduction to Theoretical Statistics (4 units)
- Advanced students may replace with STATS 270 or 300A.

- STATS 203: Regression Models and ANOVA (3 units)
- Advanced students may replace with STATS 305A.

- STATS 217: Introduction to Stochastic Processes I (3 units)
- Advanced students may replace with STATS 219 or 310B.

Students must take two advanced courses in probability or stochastic processes when replacing both STATS 118 and STATS 217.

Students may NOT enroll in STATS 118 AFTER completion of any of the following: STATS 200, 218, 219, 317, 310 A,B,C. Students may NOT enroll in STATS 200 AFTER completion of any course in the STATS 300 series.

**Example Sequences:**

- Standard: 118 - 200 - 217 - 203
- Stat Undergrad: 200/270 - 217 - 218 - 305A
- Math Undergrad: 310A - 310B - 200/300A - 305A

### Statistics Depth

(15 units) Must be taken for a letter grade.

- 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

- Lecture-based courses with cross-listings in other departments satisfy the statistics depth requirement, e.g. STATS229/CS229.

### Linear Algebra

(3-4 units) Must be taken for a letter grade.

- MATH 104: Applied Matrix Theory
- Advanced students may replace with MATH 113 or CME 302 or EE 364A.

### Programming

(3-4 units) Must be taken for a letter grade.

- CS 106B: Programming Abstractions
- Advanced students may replace with CS 107 or CME 108.

Substitution of other courses in Computer Science may be made with consent of the advisor.

### Breadth

(3 courses) May be taken for CR/S.

Breadth courses that provide the application of or a range of other disciplines to the degree may be chosen as elective units to complete the degree requirements.

The advisor may authorize other graduate courses (200 or above) if they provide skills relevant to degree requirements or deal primarily with an application of statistics or probability and do not significantly overlap (repeat) courses in the studentâ€™s program.

- Three courses in related fields numbered 200 or higher.
- Students may enroll in up to six units (combined) of the following workshops, training seminars, and independent research credit to fulfill breadth/elective coursework.
- STATS 260 series: Workshop in Biostatistics (1-2 units)
- STATS 242: NeuroTech Training Seminar (1 unit)
- STATS 249: Experimental Immersion in Neuroscience (1 unit)
- STATS 352: Topics in Computing for Data Science (1 unit)
- STATS 264: Foundations of Statistical and Scientific Inference (EPI 264)
- STATS 285: Massive Computational Experiments, Painlessly
- 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)

There is sufficient flexibility to accommodate students with interests in applications to business, computing, economics, engineering, health, operations research, and biological and social sciences.

List of suggested courses available from the programâ€™s webpage.

Courses that fulfill elective units may be taken concerning CR (credit) or S (satisfactory).

Courses below 200 level are not acceptable with the following exceptions:

- Math 104
- Math 113
- CS 106B
- CS 107
- CME 108
- STATS 118