Statistics

STATS 32. Introduction to R for Undergraduates. 1 Unit.

This short course runs for weeks one through five of the quarter. It is recommended for undergraduate students who want to use R in the humanities or social sciences and for students who want to learn the basics of R programming. The goal of the short course is to familiarize students with R's tools for data analysis. Lectures will be interactive with a focus on learning by example, and assignments will be application-driven. No prior programming experience is needed. Topics covered include basic data structures, File I/O, data transformation and visualization, simple statistical tests, etc, and some useful packages in R. Prerequisite: undergraduate student. Priority given to non-engineering students. Laptops necessary for use in class.

STATS 48N. Riding the Data Wave. 3 Units.

Imagine collecting a bit of your saliva and sending it in to one of the personalized genomics company: for very little money you will get back information about hundreds of thousands of variable sites in your genome. Records of exposure to a variety of chemicals in the areas you have lived are only a few clicks away on the web; as are thousands of studies and informal reports on the effects of different diets, to which you can compare your own. What does this all mean for you? Never before in history humans have recorded so much information about themselves and the world that surrounds them. Nor has this data been so readily available to the lay person. Expression as "data deluge'' are used to describe such wealth as well as the loss of proper bearings that it often generates. How to summarize all this information in a useful way? How to boil down millions of numbers to just a meaningful few? How to convey the gist of the story in a picture without misleading oversimplifications? To answer these questions we need to consider the use of the data, appreciate the diversity that they represent, and understand how people instinctively interpret numbers and pictures. During each week, we will consider a different data set to be summarized with a different goal. We will review analysis of similar problems carried out in the past and explore if and how the same tools can be useful today. We will pay attention to contemporary media (newspapers, blogs, etc.) to identify settings similar to the ones we are examining and critique the displays and summaries there documented. Taking an experimental approach, we will evaluate the effectiveness of different data summaries in conveying the desired information by testing them on subsets of the enrolled students.
Same as: BIODS 48N

STATS 60. Introduction to Statistical Methods: Precalculus. 5 Units.

Techniques for organizing data, computing, and interpreting measures of central tendency, variability, and association. Estimation, confidence intervals, tests of hypotheses, t-tests, correlation, and regression. Possible topics: analysis of variance and chi-square tests, computer statistical packages.
Same as: PSYCH 10, STATS 160

STATS 100. Mathematics of Sports. 3 Units.

This course will teach you how statistics and probability can be applied in sports, in order to evaluate team and individual performance, build optimal in-game strategies and ensure fairness between participants. Topics will include examples drawn from multiple sports such as basketball, baseball, soccer, football and tennis. The course is intended to focus on data-based applications, and will involve computations in R with real data sets via tutorial sessions and homework assignments. Prereqs: No statistical or programming background is assumed, but introductory courses, e.g, STATS 60,101 or 116, are recommended. A prior knowledge of Linear Algebra (e.g., MATH 51) and basic probability is strongly recommended.

STATS 101. Data Science 101. 5 Units.

https://statweb.stanford.edu/~tibs/stat101.html This course will provide a hands-on introduction to statistics and data science. Students will engage with the fundamental ideas in inferential and computational thinking. Each week, we will explore a core topic comprising three lectures and two labs (a module), in which students will manipulate real-world data and learn about statistical and computational tools. Students will engage in statistical computing and visualization with current data analytic software (Jupyter, R). The objectives of this course are to have students (1) be able to connect data to underlying phenomena and to think critically about conclusions drawn from data analysis, and (2) be knowledgeable about programming abstractions so that they can later design their own computational inferential procedures. No programming or statistical background is assumed. Freshmen and sophomores interested in data science, computing and statistics are encouraged to attend. Open to graduates as well.

STATS 110. Statistical Methods in Engineering and the Physical Sciences. 5 Units.

Introduction to statistics for engineers and physical scientists. Topics: descriptive statistics, probability, interval estimation, tests of hypotheses, nonparametric methods, linear regression, analysis of variance, elementary experimental design. Prerequisite: one year of calculus.

STATS 116. Theory of Probability. 4 Units.

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.

STATS 141. Biostatistics. 5 Units.

Introductory statistical methods for biological data: describing data (numerical and graphical summaries); introduction to probability; and statistical inference (hypothesis tests and confidence intervals). Intermediate statistical methods: comparing groups (analysis of variance); analyzing associations (linear and logistic regression); and methods for categorical data (contingency tables and odds ratio). Course content integrated with statistical computing in R.
Same as: BIO 141

STATS 155. Modern Statistics for Modern Biology. 3 Units.

Application based course in nonparametric statistics. Modern toolbox of visualization and statistical methods for the analysis of data, examples drawn from immunology, microbiology, cancer research and ecology. Methods covered include multivariate methods (PCA and extensions), sparse representations (trees, networks, contingency tables) as well as nonparametric testing (Bootstrap, permutation and Monte Carlo methods). Hands on, use R and cover many Bioconductor packages. Prerequisite: Working knowledge of R and two core Biology courses. Note that the 155 offering is a writing intensive course for undergraduates only and requires instructor consent. (WIM).
Same as: BIOS 221, STATS 256, STATS 366

STATS 160. Introduction to Statistical Methods: Precalculus. 5 Units.

Techniques for organizing data, computing, and interpreting measures of central tendency, variability, and association. Estimation, confidence intervals, tests of hypotheses, t-tests, correlation, and regression. Possible topics: analysis of variance and chi-square tests, computer statistical packages.
Same as: PSYCH 10, STATS 60

STATS 167. Probability: Ten Great Ideas About Chance. 4 Units.

Foundational approaches to thinking about chance in matters such as gambling, the law, and everyday affairs. Topics include: chance and decisions; the mathematics of chance; frequencies, symmetry, and chance; Bayes great idea; chance and psychology; misuses of chance; and harnessing chance. Emphasis is on the philosophical underpinnings and problems. Prerequisite: exposure to probability or a first course in statistics at the level of STATS 60 or 116.
Same as: PHIL 166, PHIL 266, STATS 267

STATS 191. Introduction to Applied Statistics. 3 Units.

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.

STATS 195. Introduction to R. 1 Unit.

This short course runs for four weeks and is offered in fall and spring. It is recommended for students who want to use R in statistics, science or engineering courses, and for students who want to learn the basics of data science with R. The goal of the short course is to familiarize students with some of the most important R tools for data analysis. Lectures will focus on learning by example and assignments will be application-driven. No prior programming experience is assumed.
Same as: CME 195

STATS 196A. Multilevel Modeling Using R. 1 Unit.

See http://rogosateaching.com/stat196/ . Multilevel data analysis examples using R. Topics include: two-level nested data, growth curve modeling, generalized linear models for counts and categorical data, nonlinear models, three-level analyses.
Same as: EDUC 401D

STATS 199. Independent Study. 1-15 Unit.

For undergraduates.

STATS 200. Introduction to Statistical Inference. 4 Units.

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 of their choosing in addition to the main lecture.

STATS 202. Data Mining and Analysis. 3 Units.

Data mining is used to discover patterns and relationships in data. Emphasis is on large complex data sets such as those in very large databases or through web mining. Topics: decision trees, association rules, clustering, case based methods, and data visualization. Prereqs: Introductory courses in statistics or probability (e.g., STATS 60), linear algebra (e.g., MATH 51), and computer programming (e.g., CS 105).

STATS 203. Introduction to Regression Models and Analysis of Variance. 3 Units.

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. Prerequisites: A post-calculus introductory probability course, e.g. STATS 116, basic computer programming knowledge, some familiarity with matrix algebra, and a pre- or co-requisite post-calculus mathematical statistics course, e.g. STATS 200.

STATS 203V. Introduction to Regression Models and Analysis of Variance. 3 Units.

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. This course is offered remotely only via video segments (MOOC style). TAs will host remote weekly office hours using an online platform such as Zoom. Prerequisites: A post-calculus introductory probability course, e.g. STATS 116, basic computer programming knowledge, some familiarity with matrix algebra, and a pre- or co-requisite post-calculus mathematical statistics course, e.g. STATS 200.

STATS 204. Sampling. 3 Units.

How best to take data and where to sample it. Examples include surveys and sampling from data warehouses. Emphasis is on methods for finite populations. Topics: simple random sampling, stratified sampling, cluster sampling, ratio and regression estimators, two stage sampling.

STATS 205. Introduction to Nonparametric Statistics. 3 Units.

Nonparametric regression and nonparametric density estimation, modern nonparametric techniques, nonparametric confidence interval estimates, nearest neighbor algorithms (with non-linear features), wavelet, bootstrap. Nonparametric analogs of the one- and two-sample t-tests and analysis of variance.

STATS 206. Applied Multivariate Analysis. 3 Units.

Introduction to the statistical analysis of several quantitative measurements on each observational unit. Emphasis is on concepts, computer-intensive methods. Examples from economics, education, geology, psychology. Topics: multiple regression, multivariate analysis of variance, principal components, factor analysis, canonical correlations, multidimensional scaling, clustering. Pre- or corequisite: 200.

STATS 207. Introduction to Time Series Analysis. 3 Units.

Time series models used in economics and engineering. Trend fitting, autoregressive and moving average models and spectral analysis, Kalman filtering, and state-space models. Seasonality, transformations, and introduction to financial time series. Prerequisite: basic course in Statistics at the level of 200.

STATS 208. Bootstrap, Cross-Validation, and Sample Re-use. 3 Units.

By re-using the sample data, sometimes in ingenious ways, we can evaluate the accuracy of predictions, test the significance of a conclusion, place confidence bounds on an unknown parameter, select the best prediction architecture, and develop more accurate predictors. In this course, we will describe the many ways that samples get reused to achieve these goals, including the bootstrap, the parametric bootstrap, cross-validation, conformal prediction, random forests, and sample splitting. We also develop basic theory justifying such methods. Prerequisite: course in statistics or probability.

STATS 209A. Topics in Causal Inference. 3 Units.

This course introduces the fundamental ideas and methods in causal inference, and surveys a broad range of problems and applications. Emphasis will be on framing causal problems and identifying causal effects in both randomized experiments and observational studies. Topics will include: the potential outcomes framework; randomization-based inference and covariate adjustment; matching, and IPW; instrumental variables, regression discontinuity and synthetic ncontrols. Examples and applications will be taken from the fields of education, political science, economics, public health and digital marketing.
Same as: MS&E 327

STATS 209B. Applications of Causal Inference Methods. 2 Units.

See http://rogosateaching.com/stat209/. Application of potential outcomes formulation for causal inference to research settings including: mediation, compliance adjustments, time-1 time-2 designs, encouragement designs, heterogeneous treatment effects, aggregated data, instrumental variables, analysis of covariance regression adjustments, and implementations of matching methods. Prerequisite: STATS 209A/MSE 327 or other introduction to causal inference methods. (Formerly HRP 239).
Same as: EDUC 260A, EPI 239

STATS 211. Meta-research: Appraising Research Findings, Bias, and Meta-analysis. 3 Units.

Open to graduate, medical, and undergraduate students. Appraisal of the quality and credibility of research findings; evaluation of sources of bias. Meta-analysis as a quantitative (statistical) method for combining results of independent studies. Examples from medicine, epidemiology, genomics, ecology, social/behavioral sciences, education. Collaborative analyses. Project involving generation of a meta-research project or reworking and evaluation of an existing published meta-analysis. Prerequisite: knowledge of basic statistics.
Same as: CHPR 206, EPI 206, MED 206

STATS 214. Machine Learning Theory. 3 Units.

How do we use mathematical thinking to design better machine learning methods? This course focuses on developing mathematical tools for answering these questions. This course will cover fundamental concepts and principled algorithms in machine learning. We have a special focus on modern large-scale non-linear models such as matrix factorization models and deep neural networks. In particular, we will cover concepts and phenomenon such as uniform convergence, double descent phenomenon, implicit regularization, and problems such as matrix completion, bandits, and online learning (and generally sequential decision making under uncertainty). Prerequisites: linear algebra (MATH 51 or CS 205), probability theory (STATS 116, MATH 151 or CS 109), and machine learning (CS 229, STATS 229, or STATS 315A).
Same as: CS 229M

STATS 215. Statistical Models in Biology. 3 Units.

Poisson and renewal processes, Markov chains in discrete and continuous time, branching processes, diffusion. Applications to models of nucleotide evolution, recombination, the Wright-Fisher process, coalescence, genetic mapping, sequence analysis. Theoretical material approximately the same as in STATS 217, but emphasis is on examples drawn from applications in biology, especially genetics. Prerequisite: 116 or equivalent.

STATS 216. Introduction to Statistical Learning. 3 Units.

Overview of supervised learning, with a focus on regression and classification methods. Syllabus includes: linear and polynomial regression, logistic regression and linear discriminant analysis;cross-validation and the bootstrap, model selection and regularization methods (ridge and lasso); nonlinear models, splines and generalized additive models; tree-based methods, random forests and boosting; support-vector machines; Some unsupervised learning: principal components and clustering (k-means and hierarchical). Computing is done in R, through tutorial sessions and homework assignments. This math-light course is offered via video segments (MOOC style), and in-class problem solving sessions. Prereqs: Introductory courses in statistics or probability (e.g., STATS 60 or STATS 101), linear algebra (e.g., MATH 51), and computer programming (e.g., CS 105).

STATS 216V. Introduction to Statistical Learning. 3 Units.

Overview of supervised learning, with a focus on regression and classification methods. Syllabus includes: linear and polynomial regression, logistic regression and linear discriminant analysis; cross-validation and the bootstrap, model selection and regularization methods (ridge and lasso); nonlinear models, splines and generalized additive models; tree-based methods, random forests and boosting; support-vector machines; Some unsupervised learning: principal components and clustering (k-means and hierarchical). Computing is done in R, through tutorial sessions and homework assignments. This math-light course is offered remotely only via video segments (MOOC style). TAs will host remote weekly office hours using an online platform such as Zoom. There are four homework assignments, a midterm, and a final exam, all of which are administered remotely. Prereqs: Introductory courses in statistics or probability (e.g., STATS 60 or STATS 101), linear algebra (e.g., MATH 51), and computer programming (e.g., CS 105).

STATS 217. Introduction to Stochastic Processes I. 3 Units.

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. Prerequisite: a post-calculus introductory probability course e.g. STATS 116.

STATS 218. Introduction to Stochastic Processes II. 3 Units.

Renewal theory, Brownian motion, Gaussian processes, second order processes, martingales.

STATS 219. Stochastic Processes. 3 Units.

Introduction to measure theory, Lp spaces and Hilbert spaces. Random variables, expectation, conditional expectation, conditional distribution. Uniform integrability, almost sure and Lp convergence. Stochastic processes: definition, stationarity, sample path continuity. Examples: random walk, Markov chains, Gaussian processes, Poisson processes, Martingales. Construction and basic properties of Brownian motion. Prerequisite: STATS 116 or MATH 151 or equivalent. Recommended: MATH 115 or equivalent. http://statweb.stanford.edu/~adembo/math-136/.
Same as: MATH 136

STATS 220. Machine Learning Methods for Neural Data Analysis. 3 Units.

With modern high-density electrodes and optical imaging techniques, neuroscientists routinely measure the activity of hundreds, if not thousands, of cells simultaneously. Coupled with high-resolution behavioral measurements, genetic sequencing, and connectomics, these datasets offer unprecedented opportunities to learn how neural circuits function. This course will study statistical machine learning methods for analysing such datasets, including: spike sorting, calcium deconvolution, and voltage smoothing techniques for extracting relevant signals from raw data; markerless tracking methods for estimating animal pose in behavioral videos; network models for connectomics and fMRI data; state space models for analysis of high-dimensional neural and behavioral time-series; point process models of neural spike trains; and deep learning methods for neural encoding and decoding. We will develop the theory behind these models and algorithms and then apply them to real datasets in the homeworks and final project.This course is similar to STATS215: Statistical Models in Biology and STATS366: Modern Statistics for Modern Biology, but it is specifically focused on statistical machine learning methods for neuroscience data. Prerequisites: Students should be comfortable with basic probability (STATS 116) and statistics (at the level of STATS 200). This course will place a heavy emphasis on implementing models and algorithms, so coding proficiency is required.
Same as: CS 339N, NBIO 220, STATS 320

STATS 221. Random Processes on Graphs and Lattices. 3 Units.

Covering modern topics in the study of random processes on graphs and lattices. Specifically, a subset of: Random walks, electrical networks and flows. Uniform spanning trees. Percolation and self-avoiding walks. Contact process, voter model and the exclusion process. Ising, Potts, and Random-Cluster model. Random graphs. Prerequisites: MATH 115 (or equivalent), STAT 217 (or equivalent).

STATS 222. Statistical Methods for Longitudinal Research. 2 Units.

See http://rogosateaching.com/stat222/. Research designs and statistical procedures for time-ordered (repeated-measures) data. The analysis of longitudinal panel data is central to empirical research on learning, development, aging, and the effects of interventions. Topics include: measurement of change, growth curve models, analysis of durations including survival analysis, experimental and non-experimental group comparisons, reciprocal effects, stability. Prerequisite: intermediate statistical methods.
Same as: EDUC 351A

STATS 229. Machine Learning. 3-4 Units.

Topics: statistical pattern recognition, linear and non-linear regression, non-parametric methods, exponential family, GLMs, support vector machines, kernel methods, deep learning, model/feature selection, learning theory, ML advice, clustering, density estimation, EM, dimensionality reduction, ICA, PCA, reinforcement learning and adaptive control, Markov decision processes, approximate dynamic programming, and policy search. Prerequisites: knowledge of basic computer science principles and skills at a level sufficient to write a reasonably non-trivial computer program in Python/numpy, familiarity with probability theory to the equivalency of CS109 or STATS116, and familiarity with multivariable calculus and linear algebra to the equivalency of MATH51.
Same as: CS 229

STATS 237. Investment Portfolios, Derivative Securities, and Risk Measures. 3 Units.

Asset returns and their volatilities. Markowitz portfolio theory, capital asset pricing model, multifactor pricing models. Measures of market risk and statistical models and methods for their estimation and backtesting. Financial derivatives and hedging. Black-Scholes pricing of European options and implied volatilities. Prerequisite: STATS 116 or equivalent.

STATS 237P. Investment Portfolios, Derivative Securities, and Risk Measures. 3 Units.

For SCPD students; see STATS237.

STATS 240. Statistical Methods in Finance. 3 Units.

(SCPD students register for 240P.) Regression analysis and applications to investment models. Principal components and multivariate analysis. Likelihood inference and Bayesian methods. Financial time series. Estimation and modeling of volatilities. Statistical methods for portfolio management. Prerequisite: STATS 200 or equivalent.

STATS 240P. Statistical Methods in Finance. 3 Units.

For SCPD students; see 240.

STATS 241. Data-driven Financial Econometrics. 3 Units.

(SCPD students register for 241P) Substantive and empirical modeling approaches in options, interest rate, and credit markets. Nonlinear least squares, logistic regression and generalized linear models. Nonparametric regression and model selection. Multivariate time series modeling and forecasting. Vector autoregressive models and cointegration. Risk measures, models and analytics. Prerequisite or corequisite: STATS 240 or equivalent.

STATS 241P. Data-driven Financial Econometrics. 3 Units.

For SCPD students; see STATS241.

STATS 242. NeuroTech Training Seminar. 1 Unit.

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.
Same as: NSUR 239

STATS 243. Risk Analytics and Management in Finance and Insurance. 2-4 Units.

Market risk and credit risk, credit markets. Back testing, stress testing and Monte Carlo methods. Logistic regression, generalized linear models and generalized mixed models. Loan prepayment and default as competing risks. Survival and hazard functions, correlated default intensities, frailty and contagion. Risk surveillance, early warning and adaptive control methodologies. Banking and bank regulation, asset and liability management. Prerequisite: STATS 240 or equivalent.
Same as: CME 243

STATS 243P. Risk Analytics and Management in Finance and Insurance. 3 Units.

For SCPD students; see STATS243.

STATS 244. Quantitative Trading: Algorithms, Data, and Optimization. 2-4 Units.

Statistical trading rules and performances evaluation. Active portfolio management and dynamic investment strategies. Data analytics and models of transactions data. Limit order book dynamics in electronic exchanges. Algorithmic trading, informatics, and optimal execution. Market making and inventory control. Risk management and regulatory issues. Prerequisites: STATS 240 or equivalent.

STATS 244P. Quantitative Trading: Algorithms, Data and Optimization. 3 Units.

For SCPD students; see 244.

STATS 245. Data, Models and Applications to Healthcare Analytics. 3 Units.

Topics on fundamentals of data science, biological and statistical models, application to medical product safety evaluation, health risk models and their evaluation, benefit-risk assessment and multi-criteria decision analytics. Applications to environmental health, nutritional epidemiology, wellness and prevention will also be discussed. Prerequisite: Graduate students - STATS 202 or 216, or CS 229; Undergraduate students - consent of instructor.

STATS 245P. Data, Models, and Applications to Healthcare Analytics. 3 Units.

For SCPD students; see STATS245.

STATS 248. Clinical Trial Design in the Age of Precision Medicine and Health. 3 Units.

Overview of requirements, designs, and statistical foundations for traditional Phase I, II, and III clinical trials for medical product approval and Phase IV postmarketing studies for safety evaluation. As these methods cost too much and take too much time in the era of precision medicine and precision health, this course then introduces innovative designs that have been developed for affordable clinical trials, which can be completed within reasonable time constraints and which have been encouraged by regulatory agencies. Prerequisites: Working knowledge of statistics and R.
Same as: BIODS 248, BIODS 248P, BIOMEDIN 248

STATS 249. Experimental Immersion in Neuroscience. 1 Unit.

This course provides students from technical backgrounds (e.g., physics, applied physics, electrical or chemical engineering, bioengineering, computer science, statistics) the opportunity to learn how they can apply their expertise to advancing experimental research in the neurosciences. Students will visit one neuroscience lab per week to watch experiments, understand the technical apparatus and animal models being used, discuss the questions being addressed, and interact with students and others conducting the research. This course is strongly encouraged for students who wish to apply to the NeuroTech graduate training program.
Same as: NSUR 249

STATS 250. Mathematical Finance. 3 Units.

Stochastic models of financial markets. Forward and futures contracts. European options and equivalent martingale measures. Hedging strategies and management of risk. Term structure models and interest rate derivatives. Optimal stopping and American options. Corequisites: MATH 236 and 227 or equivalent.nnNOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing information about relevant background such as performance in prior coursework, reading, etc.
Same as: MATH 238

STATS 253. Analysis of Spatial and Temporal Data. 3 Units.

A unified treatment of methods for spatial data, time series, and other correlated data from the perspective of regression with correlated errors. Two main paradigms for dealing with autocorrelation: covariance modeling (kriging) and autoregressive processes. Bayesian methods. Prerequisites: applied linear algebra (MATH 103 or equivalent), statistical estimation (STATS 200 or CS 229), and linear regression (STATS 203 or equivalent).

STATS 256. Modern Statistics for Modern Biology. 3 Units.

Application based course in nonparametric statistics. Modern toolbox of visualization and statistical methods for the analysis of data, examples drawn from immunology, microbiology, cancer research and ecology. Methods covered include multivariate methods (PCA and extensions), sparse representations (trees, networks, contingency tables) as well as nonparametric testing (Bootstrap, permutation and Monte Carlo methods). Hands on, use R and cover many Bioconductor packages. Prerequisite: Working knowledge of R and two core Biology courses. Note that the 155 offering is a writing intensive course for undergraduates only and requires instructor consent. (WIM).
Same as: BIOS 221, STATS 155, STATS 366

STATS 260A. Workshop in Biostatistics. 1-2 Unit.

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.
Same as: BIODS 260A

STATS 260B. Workshop in Biostatistics. 1-2 Unit.

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.
Same as: BIODS 260B

STATS 260C. Workshop in Biostatistics. 1-2 Unit.

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.
Same as: BIODS 260C

STATS 261. Intermediate Biostatistics: Analysis of Discrete Data. 3 Units.

(Formerly HRP 261) Methods for analyzing data from case-control and cross-sectional studies: the 2x2 table, chi-square test, Fisher's exact test, odds ratios, Mantel-Haenzel methods, stratification, tests for matched data, logistic regression, conditional logistic regression. Emphasis is on data analysis in SAS or R. Special topics: cross-fold validation and bootstrap inference.
Same as: BIOMEDIN 233, EPI 261

STATS 262. Intermediate Biostatistics: Regression, Prediction, Survival Analysis. 3 Units.

(Formerly HRP 262) Methods for analyzing longitudinal data. Topics include Kaplan-Meier methods, Cox regression, hazard ratios, time-dependent variables, longitudinal data structures, profile plots, missing data, modeling change, MANOVA, repeated-measures ANOVA, GEE, and mixed models. Emphasis is on practical applications. Prerequisites: basic ANOVA and linear regression.
Same as: EPI 262

STATS 263. Design of Experiments. 3 Units.

Experiments vs observation. Confounding. Randomization. ANOVA.Blocking. Latin squares. Factorials and fractional factorials. Split plot. Response surfaces. Mixture designs. Optimal design. Central composite. Box-Behnken. Taguchi methods. Computer experiments and space filling designs. Prerequisites: probability at STATS 116 level or higher, and at least one course in linear models.
Same as: STATS 363

STATS 264. Foundations of Statistical and Scientific Inference. 1 Unit.

(Formerly HRP 264) The course will consist of readings and discussion of foundational papers and book sections in the domains of statistical and scientific inference. Topics to be covered include philosophy of science, interpretations of probability, Bayesian and frequentist approaches to statistical inference and current controversies about the proper use of p-values and research reproducibility. Recommended preparation: At least 2 quarters of biostatistics and one of epidemiology. Intended for second year Masters students or PhD students with at least 1 year of preceding graduate training.
Same as: EPI 264

STATS 266. Advanced Statistical Methods for Observational Studies. 2-3 Units.

Design principles and statistical methods for observational studies. Topics include: matching methods, sensitivity analysis, and instrumental variables. 3 unit registration requires a small project and presentation. Computing is in R. Pre-requisites: EPI 261 and 262 or STATS 209 (EPI 239), or equivalent. See http://rogosateaching.com/somgen290/.
Same as: CHPR 266, EDUC 260B, EPI 292

STATS 267. Probability: Ten Great Ideas About Chance. 4 Units.

Foundational approaches to thinking about chance in matters such as gambling, the law, and everyday affairs. Topics include: chance and decisions; the mathematics of chance; frequencies, symmetry, and chance; Bayes great idea; chance and psychology; misuses of chance; and harnessing chance. Emphasis is on the philosophical underpinnings and problems. Prerequisite: exposure to probability or a first course in statistics at the level of STATS 60 or 116.
Same as: PHIL 166, PHIL 266, STATS 167

STATS 270. A Course in Bayesian Statistics. 3 Units.

This course will treat Bayesian statistics at a relatively advanced level. Assuming familiarity with standard probability and multivariate distribution theory, we will provide a discussion of the mathematical and theoretical foundation for Bayesian inferential procedures. In particular, we will examine the construction of priors and the asymptotic properties of likelihoods and posterior distributions. The discussion will include but will not be limited to the case of finite dimensional parameter space. There will also be some discussions on the computational algorithms useful for Bayesian inference. Prerequisites: STATS 116 or equivalent probability course, plus basic programming knowledge; basic calculus, analysis and linear algebra strongly recommended; STATS 200 or equivalent statistical theory course desirable.
Same as: STATS 370

STATS 271. Applied Bayesian Statistics. 3 Units.

This course is a modern treatment of applied Bayesian statistics with a focus on high-dimensional problems. We will study a collection of canonical methods that see heavy use in applications, including high-dimensional linear and generalized linear models, hierarchical/random effects models, Gaussian processes, variable-dimension and Dirichlet process mixtures, graphical models, and methods used in Bayesian inverse problems. Each method will be accompanied by one or more motivating datasets. Through these examples the course will cover: (1) Bayesian hypothesis testing, multiplicity correction, selection, shrinkage, and model averaging; (2) prior choice; (3) Frequentist properties of Bayesian procedures in high dimensions; and (4) computation by Markov chain Monte Carlo, including constructing efficient Gibbs, Metropolis, and more exotic samplers, empirical convergence analysis, strategies for scaling computation to high dimensions (approximations, divide-and-conquer, minibatching, et cetera), and the theory of convergence rates.
Same as: STATS 371

STATS 281. Statistical Analysis of Fine Art. 3 Units.

This course presents the application of rigorous statistical analysis, machine learning, and data analysis to problems in the history and interpretation of fine art paintings, drawings, and other two-dimensional artworks. The course focuses on the aspects of these problems that are unlike those addressed widely elsewhere in statistical image analysis, such as applied to photographs, videos, and medical images. These novel problems include statistical analysis of brushstrokes and marks, medium, inferring artists¿ working methods, compositional principles, stylometry (quantification of style), the tracing of artistic influence, and art attribution and authentication. The course revisits classic problems, such as image-based object recognition and scene description, but in the environment of highly non-realistic, stylized artworks.

STATS 285. Massive Computational Experiments, Painlessly. 2 Units.

Ambitious Data Science requires massive computational experimentation; the entry ticket for a solid PhD in some fields is now to conduct experiments involving 1 Million CPU hours. Recently several groups have created efficient computational environments that make it painless to run such massive experiments. This course reviews state-of-the-art practices for doing massive computational experiments on compute clusters in a painless and reproducible manner. Students will learn how to automate their computing experiments first of all using nuts-and-bolts tools such as Perl and Bash, and later using available comprehensive frameworks such as ClusterJob and CodaLab, which enables them to take on ambitious Data Science projects. The course also features few guest lectures by renowned scientists in the field of Data Science. Students should have a familiarity with computational experiments and be facile in some high-level computer language such as R, Matlab, or Python.

STATS 290. Computing for Data Science. 3 Units.

Programming and computing techniques for the requirements of data science: acquisition and organization of data; visualization, modelling and inference for scientific applications; presentation and interactive communication of results. Emphasis on computing for substantial projects. Software development with emphasis on R, plus other key software tools. Prerequisites: Programming experience including familiarity with R; computing at least at the level of CS 106; statistics at the level of STATS 110 or 141.

STATS 298. Industrial Research for Statisticians. 1 Unit.

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.

STATS 299. Independent Study. 1-5 Unit.

For Statistics M.S. students only. Reading or research program under the supervision of a Statistics faculty member. May be repeated for credit.

STATS 300A. Theory of Statistics I. 3 Units.

Finite sample optimality of statistical procedures; Decision theory: loss, risk, admissibility; Principles of data reduction: sufficiency, ancillarity, completeness; Statistical models: exponential families, group families, nonparametric families; Point estimation: optimal unbiased and equivariant estimation, Bayes estimation, minimax estimation; Hypothesis testing and confidence intervals: uniformly most powerful tests, uniformly most accurate confidence intervals, optimal unbiased and invariant tests. Prerequisites: Real analysis, introductory probability (at the level of STATS 116), and introductory statistics.

STATS 300B. Theory of Statistics II. 3 Units.

Elementary decision theory; loss and risk functions, Bayes estimation; UMVU estimator, minimax estimators, shrinkage estimators. Hypothesis testing and confidence intervals: Neyman-Pearson theory; UMP tests and uniformly most accurate confidence intervals; use of unbiasedness and invariance to eliminate nuisance parameters. Large sample theory: basic convergence concepts; robustness; efficiency; contiguity, locally asymptotically normal experiments; convolution theorem; asymptotically UMP and maximin tests. Asymptotic theory of likelihood ratio and score tests. Rank permutation and randomization tests; jackknife, bootstrap, subsampling and other resampling methods. Further topics: sequential analysis, optimal experimental design, empirical processes with applications to statistics, Edgeworth expansions, density estimation, time series.

STATS 300C. Theory of Statistics III. 3 Units.

Decision theory formulation of statistical problems. Minimax, admissible procedures. Complete class theorems ("all" minimax or admissible procedures are "Bayes"), Bayes procedures, conjugate priors, hierarchical models. Bayesian non parametrics: diaichlet, tail free, polya trees, bayesian sieves. Inconsistency of bayes rules.

STATS 302. Qualifying Exams Workshop. 5-10 Units.

Prepares Statistics Ph.D. students for the qualifying exams by reviewing relevant course topics and problem solving strategies.

STATS 303. Statistics Faculty Research Presentations. 1 Unit.

For Statistics first and second year PhD students only. Discussion of statistics topics and research areas; consultation with PhD advisors.

STATS 305A. Applied Statistics I. 3 Units.

Statistics of real valued responses. Review of multivariate normal distribution theory. Univariate regression. Multiple regression. Constructing features from predictors. Geometry and algebra of least squares: subspaces, projections, normal equations, orthogonality, rank deficiency, Gauss-Markov. Gram-Schmidt, the QR decomposition and the SVD. Interpreting coefficients. Collinearity. Dependence and heteroscedasticity. Fits and the hat matrix. Model diagnostics. Model selection, Cp/AIC and crossvalidation, stepwise, lasso. Multiple comparisons. ANOVA, fixed and random effects. Use of bootstrap and permutations. Emphasis on problem sets involving substantive computations with data sets. Prerequisites: consent of instructor, 116, 200, applied statistics course, CS 106A, MATH 114.

STATS 305B. Applied Statistics II: Generalized Linear Models, Survival Analysis, and Exponential Families. 3 Units.

This course uses exponential family structure to motivate generalized linear models and other useful applied techniques including survival analysis methods and Bayes and empirical Bayes analyses. The lectures are based on a forthcoming book whose notes will be distributed. Prerequisites: 305A or consent of the instructor.

STATS 305C. Applied Statistics III. 3 Units.

Methods for multivariate responses. Theory, computation and practice for multivariate statistical tools. Multivariate Gaussian and undirected graphical models, graphical displays. Hotelling's T-squared, principal components, canonical correlations, linear discriminant analysis, correspondence analysis, and recent variants of these. Hierarchical and k-means clustering. Bi-clustering. Factor analysis and independent component analysis. Topic modeling. Multidimensional scaling and variants (e.g., Isomap, spectral clustering, t-SNE). Matrix completion. Extensive work with data involving programming, ideally in R. Prerequisites: STATS 305A and STATS 305B or consent of the instructor.

STATS 310A. Theory of Probability I. 3 Units.

Mathematical tools: sigma algebras, measure theory, connections between coin tossing and Lebesgue measure, basic convergence theorems. Probability: independence, Borel-Cantelli lemmas, almost sure and Lp convergence, weak and strong laws of large numbers. Large deviations. Weak convergence; central limit theorems; Poisson convergence; Stein's method. Prerequisites: STATS 116, MATH 171.
Same as: MATH 230A

STATS 310B. Theory of Probability II. 3 Units.

Conditional expectations, discrete time martingales, stopping times, uniform integrability, applications to 0-1 laws, Radon-Nikodym Theorem, ruin problems, etc. Other topics as time allows selected from (i) local limit theorems, (ii) renewal theory, (iii) discrete time Markov chains, (iv) random walk theory,n(v) ergodic theory. http://statweb.stanford.edu/~adembo/stat-310b. Prerequisite: 310A or MATH 230A.
Same as: MATH 230B

STATS 310C. Theory of Probability III. 3 Units.

Continuous time stochastic processes: martingales, Brownian motion, stationary independent increments, Markov jump processes and Gaussian processes. Invariance principle, random walks, LIL and functional CLT. Markov and strong Markov property. Infinitely divisible laws. Some ergodic theory. Prerequisite: 310B or MATH 230B. http://statweb.stanford.edu/~adembo/stat-310c/.
Same as: MATH 230C

STATS 311. Information Theory and Statistics. 3 Units.

Information theoretic techniques in probability and statistics. Fano, Assouad,nand Le Cam methods for optimality guarantees in estimation. Large deviationsnand concentration inequalities (Sanov's theorem, hypothesis testing, thenentropy method, concentration of measure). Approximation of (Bayes) optimalnprocedures, surrogate risks, f-divergences. Penalized estimators and minimumndescription length. Online game playing, gambling, no-regret learning. Prerequisites: EE 276 (or equivalent) or STATS 300A.
Same as: EE 377

STATS 314A. Advanced Statistical Theory. 3 Units.

Covers a range of topics, including: empirical processes, asymptotic efficiency, uniform convergence of measures, contiguity, resampling methods, Edgeworth expansions.

STATS 315A. Modern Applied Statistics: Learning. 3 Units.

Overview of supervised learning. Linear regression and related methods. Model selection, least angle regression and the lasso, stepwise methods. Classification. Linear discriminant analysis, logistic regression, and support vector machines (SVMs). Basis expansions, splines and regularization. Kernel methods. Generalized additive models. Kernel smoothing. Gaussian mixtures and the EM algorithm. Model assessment and selection: crossvalidation and the bootstrap. Pathwise coordinate descent. Sparse graphical models. Prerequisites: STATS 305A, 305B, 305C or consent of instructor.

STATS 315B. Modern Applied Statistics: Data Mining. 3 Units.

Two-part sequence. New techniques for predictive and descriptive learning using ideas that bridge gaps among statistics, computer science, and artificial intelligence. Emphasis is on statistical aspects of their application and integration with more standard statistical methodology. Predictive learning refers to estimating models from data with the goal of predicting future outcomes, in particular, regression and classification models. Descriptive learning is used to discover general patterns and relationships in data without a predictive goal, viewed from a statistical perspective as computer automated exploratory analysis of large complex data sets.

STATS 316. Stochastic Processes on Graphs. 1-3 Unit.

Local weak convergence, Gibbs measures on trees, cavity method, and replica symmetry breaking. Examples include random k-satisfiability, the assignment problem, spin glasses, and neural networks. Prerequisite: 310A or equivalent. https://web.stanford.edu/~montanar/TEACHING/Stat316/stat316.html.

STATS 317. Stochastic Processes. 3 Units.

Semimartingales, stochastic integration, Ito's formula, Girsanov's theorem. Gaussian and related processes. Stationary/isotropic processes. Integral geometry and geometric probability. Maxima of random fields and applications to spatial statistics and imaging.

STATS 318. Modern Markov Chains. 3 Units.

Tools for understanding Markov chains as they arise in applications. Random walk on graphs, reversible Markov chains, Metropolis algorithm, Gibbs sampler, hybrid Monte Carlo, auxiliary variables, hit and run, Swedson-Wong algorithms, geometric theory, Poincare-Nash-Cheeger-Log-Sobolov inequalities. Comparison techniques, coupling, stationary times, Harris recurrence, central limit theorems, and large deviations.

STATS 319. Literature of Statistics. 1 Unit.

Literature study of topics in statistics and probability culminating in oral and written reports. May be repeated for credit.

STATS 320. Machine Learning Methods for Neural Data Analysis. 3 Units.

With modern high-density electrodes and optical imaging techniques, neuroscientists routinely measure the activity of hundreds, if not thousands, of cells simultaneously. Coupled with high-resolution behavioral measurements, genetic sequencing, and connectomics, these datasets offer unprecedented opportunities to learn how neural circuits function. This course will study statistical machine learning methods for analysing such datasets, including: spike sorting, calcium deconvolution, and voltage smoothing techniques for extracting relevant signals from raw data; markerless tracking methods for estimating animal pose in behavioral videos; network models for connectomics and fMRI data; state space models for analysis of high-dimensional neural and behavioral time-series; point process models of neural spike trains; and deep learning methods for neural encoding and decoding. We will develop the theory behind these models and algorithms and then apply them to real datasets in the homeworks and final project.This course is similar to STATS215: Statistical Models in Biology and STATS366: Modern Statistics for Modern Biology, but it is specifically focused on statistical machine learning methods for neuroscience data. Prerequisites: Students should be comfortable with basic probability (STATS 116) and statistics (at the level of STATS 200). This course will place a heavy emphasis on implementing models and algorithms, so coding proficiency is required.
Same as: CS 339N, NBIO 220, STATS 220

STATS 322. Function Estimation in White Noise. 3 Units.

Gaussian white noise model sequence space form. Hyperrectangles, quadratic convexity, and Pinsker's theorem. Minimax estimation on Lp balls and Besov spaces. Role of wavelets and unconditional bases. Linear and threshold estimators. Oracle inequalities. Optimal recovery and universal thresholding. Stein's unbiased risk estimator and threshold choice. Complexity penalized model selection. Connecting fast wavelet algorithms and theory. Beyond orthogonal bases.

STATS 325. Multivariate Analysis and Random Matrices in Statistics. 3 Units.

Topics on Multivariate Analysis and Random Matrices in Statistics (full description TBA).

STATS 334. Mathematics and Statistics of Gambling. 3 Units.

Probability and statistics are founded on the study of games of chance. Nowadays, gambling (in casinos, sports and the Internet) is a huge business. This course addresses practical and theoretical aspects. Topics covered: mathematics of basic random phenomena (physics of coin tossing and roulette, analysis of various methods of shuffling cards), odds in popular games, card counting, optimal tournament play, practical problems of random number generation. Prerequisites: Statistics 116 and 200.
Same as: MATH 231

STATS 345. Statistical and Machine Learning Methods for Genomics. 3 Units.

Introduction to statistical and computational methods for genomics. Sample topics include: expectation maximization, hidden Markov model, Markov chain Monte Carlo, ensemble learning, probabilistic graphical models, kernel methods and other modern machine learning paradigms. Rationales and techniques illustrated with existing implementations used in population genetics, disease association, and functional regulatory genomics studies. Instruction includes lectures and discussion of readings from primary literature. Homework and projects require implementing some of the algorithms and using existing toolkits for analysis of genomic datasets.
Same as: BIO 268, BIOMEDIN 245, CS 373

STATS 350. Topics in Probability Theory. 3 Units.

See http://statweb.stanford.edu/~adembo/stat-350/concentration/ Selected topics of contemporary research interest in probability theory. May be repeated once for credit. Prerequisite: 310A or equivalent.

STATS 352. Topics in Computing for Data Science. 3 Units.

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 website https://stat352.stanford.edu.

STATS 359. Topics in Mathematical Physics. 3 Units.

Covers a list of topics in mathematical physics. The specific topics may vary from year to year, depending on the instructor's discretion. Background in graduate level probability theory and analysis is desirable.
Same as: MATH 273

STATS 360. Advanced Statistical Methods for Earth System Analysis. 3 Units.

Introduction for graduate students to important issues in data analysis relevant to earth system studies. Emphasis on methodology, concepts and implementation (in R), rather than formal proofs. Likely topics include the bootstrap, non-parametric methods, regression in the presence of spatial and temporal correlation, extreme value analysis, time-series analysis, high-dimensional regressions and change-point models. Topics subject to change each year. Prerequisites: STATS 110 or equivalent.
Same as: ESS 260

STATS 361. Causal Inference. 3 Units.

This course covers statistical underpinnings of causal inference, with a focus on experimental design and data-driven decision making. Topics include randomization, potential outcomes, observational studies, propensity score methods, matching, double robustness, semiparametric efficiency, treatment heterogeneity, structural models, instrumental variables, principal stratification, mediation, regression discontinuities, synthetic controls, interference, sensitivity analysis, policy learning, dynamic treatment rules, invariant prediction, graphical models, and structure learning. We will also discuss the relevance of optimization and machine learning tools to causal inference. Prerequisite: STATS 300A, or equivalent graduate-level coursework on the theory of statistics.

STATS 362. Topic: Monte Carlo. 3 Units.

Random numbers and vectors: inversion, acceptance-rejection, copulas. Variance reduction: antithetics, stratification, control variates, importance sampling. MCMC: Markov chains, detailed balance, Metropolis-Hastings, random walk Metropolis,nnindependence sampler, Gibbs sampling, slice sampler, hybrids of Gibbs and Metropolis, tempering. Sequential Monte Carlo. Quasi-Monte Carlo. Randomized quasi-Monte Carlo. Examples, problems and motivation from Bayesian statistics,nnmachine learning, computational finance and graphics. May be repeat for credit.

STATS 363. Design of Experiments. 3 Units.

Experiments vs observation. Confounding. Randomization. ANOVA.Blocking. Latin squares. Factorials and fractional factorials. Split plot. Response surfaces. Mixture designs. Optimal design. Central composite. Box-Behnken. Taguchi methods. Computer experiments and space filling designs. Prerequisites: probability at STATS 116 level or higher, and at least one course in linear models.
Same as: STATS 263

STATS 364. Theory and Applications of Selective Inference. 3 Units.

This course focuses on the problem of inference under the presence of multiplicity or selection. Topics covered include classical topics multiple comparisons (FWER, FDR, FCR) as well as newer methods such as knockoffs. We will also cover inference when targeted parameters are determined only after inspection of the data, considering both conditional and simultaneous approaches. Both theoretical and computational considerations will be stressed throughout the course. Prerequisite: STATS 200 or equivalent.

STATS 366. Modern Statistics for Modern Biology. 3 Units.

Application based course in nonparametric statistics. Modern toolbox of visualization and statistical methods for the analysis of data, examples drawn from immunology, microbiology, cancer research and ecology. Methods covered include multivariate methods (PCA and extensions), sparse representations (trees, networks, contingency tables) as well as nonparametric testing (Bootstrap, permutation and Monte Carlo methods). Hands on, use R and cover many Bioconductor packages. Prerequisite: Working knowledge of R and two core Biology courses. Note that the 155 offering is a writing intensive course for undergraduates only and requires instructor consent. (WIM).
Same as: BIOS 221, STATS 155, STATS 256

STATS 367. Statistical Models in Genetics. 3 Units.

This course will cover statistical problems in population genetics and molecular evolution with an emphasis on coalescent theory. Special attention will be paid to current research topics, illustrating the challenges presented by genomic data obtained via high-throughput technologies. No prior knowledge of genomics is necessary. Familiarity with the R statistical package or other computing language is needed for homework assignments. Prerequisites: knowledge of probability through elementary stochastic processes and statistics through likelihood theory.

STATS 368. Empirical Process Theory and its Applications. 3 Units.

This course is on the theory of empirical processes. In the course we will focus on weak convergence of stochastic processes, M-estimation and empirical risk minimization. The course will cover topics like covering numbers and bracketing numbers, maximal inequalities, chaining and symmetrization, uniform law of large numbers and uniform central limit theorems, rates of convergence of MLEs and (penalized) least squares estimators, and concentration inequalities.

STATS 369. Methods from Statistical Physics. 3 Units.

Mathematical techniques from statistical physics have been applied with increasing success on problems form combinatorics, computer science, machine learning. These methods are non-rigorous, but in several cases they were proved to yield correct predictions. This course provides a working knowledge of these methods for non-physicists. Specific topics: the Sherrington-Kirkpatrick model; sparse regression with random designs;.

STATS 370. A Course in Bayesian Statistics. 3 Units.

This course will treat Bayesian statistics at a relatively advanced level. Assuming familiarity with standard probability and multivariate distribution theory, we will provide a discussion of the mathematical and theoretical foundation for Bayesian inferential procedures. In particular, we will examine the construction of priors and the asymptotic properties of likelihoods and posterior distributions. The discussion will include but will not be limited to the case of finite dimensional parameter space. There will also be some discussions on the computational algorithms useful for Bayesian inference. Prerequisites: STATS 116 or equivalent probability course, plus basic programming knowledge; basic calculus, analysis and linear algebra strongly recommended; STATS 200 or equivalent statistical theory course desirable.
Same as: STATS 270

STATS 371. Applied Bayesian Statistics. 3 Units.

This course is a modern treatment of applied Bayesian statistics with a focus on high-dimensional problems. We will study a collection of canonical methods that see heavy use in applications, including high-dimensional linear and generalized linear models, hierarchical/random effects models, Gaussian processes, variable-dimension and Dirichlet process mixtures, graphical models, and methods used in Bayesian inverse problems. Each method will be accompanied by one or more motivating datasets. Through these examples the course will cover: (1) Bayesian hypothesis testing, multiplicity correction, selection, shrinkage, and model averaging; (2) prior choice; (3) Frequentist properties of Bayesian procedures in high dimensions; and (4) computation by Markov chain Monte Carlo, including constructing efficient Gibbs, Metropolis, and more exotic samplers, empirical convergence analysis, strategies for scaling computation to high dimensions (approximations, divide-and-conquer, minibatching, et cetera), and the theory of convergence rates.
Same as: STATS 271

STATS 374. Large Deviations Theory. 3 Units.

Combinatorial estimates and the method of types. Large deviation probabilities for partial sums and for empirical distributions, Cramer's and Sanov's theorems and their Markov extensions. Applications in statistics, information theory, and statistical mechanics. Prerequisite: MATH 230A or STATS 310. Offered every 2-3 years. http://statweb.stanford.edu/~adembo/large-deviations/.
Same as: MATH 234

STATS 375. Mathematical problems in Machine Learning. 3 Units.

Mathematical tools to understand modern machine learning systems. Generalization in machine learning, the classical view: uniform convergence, Radamacher complexity. Generalization from stability. Implicit (algorithmic) regularization. Infinite-dimensional models: reproducing kernel Hilbert spaces. Random features approximations to kernel methods. Connections to neural networks, and neural tangent kernel. Nonparametric regression. Asymptotic behavior of wide neural networks. Properties of convolutionalnnetworks. Prerequisites: EE364A or equivalent; Stat310A or equivalent.
Same as: EE 375

STATS 376A. Information Theory. 3 Units.

(Formerly EE 376A.) Project-based course about how to measure, represent, and communicate information effectively. Why bits have become the universal currency for information exchange. How information theory bears on the design and operation of modern-day systems such as smartphones and the Internet. The role of entropy and mutual information in data compression, communication, and inference. Practical compressors and error correcting codes. The information theoretic way of thinking. Relations and applications to probability, statistics, machine learning, biological and artificial neural networks, genomics, quantum information, and blockchains. Prerequisite: a first undergraduate course in probability.
Same as: EE 276

STATS 376B. Topics in Information Theory and Its Applications. 3 Units.

Information theory establishes the fundamental limits on compression and communication over networks. The tools of information theory have also found applications in many other fields, including probability and statistics, computer science and physics. The course will cover selected topics from these applications, including communication networks, through regular lectures and student projects. Prerequisites: EE276 (Formerly EE376A).
Same as: EE 376B

STATS 385. Analyses of Deep Learning. 1 Unit.

Deep learning is a transformative technology that has delivered impressive improvements in image classification and speech recognition. Many researchers are trying to better understand how to improve prediction performance and also how to improve training methods. Some researchers use experimental techniques; others use theoretical approaches. In this course we will review both experimental and theoretical analyses of deep learning. We will have 8-10 guest lecturers as well as graded projects for those who take the course for credit.

STATS 390. Consulting Workshop. 1 Unit.

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.

STATS 397. PhD Oral Exam Workshop. 1 Unit.

For Statistics PhD students defending their dissertation.

STATS 398. Industrial Research for Statisticians. 1 Unit.

Doctoral research as in 399, but must be conducted for an off-campus employer. A final report acceptable to the advisor outlining work activity, problems investigated, key results, and any follow-up projects they expect to perform is required. The report is due at the end of the quarter in which the course is taken. May be repeated for credit. Prerequisite: Statistics Ph.D. candidate.

STATS 399. Research. 1-10 Unit.

Research work as distinguished from independent study of nonresearch character listed in 199. May be repeated for credit.

STATS 801. TGR Project. 0 Units.

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STATS 802. TGR Dissertation. 0 Units.

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