COMPUTATIONAL STATISTICS

Prerequisites & course information

Requisites: Declared in Statistics MS, Statistics PhD, Biomedical Data Science PhD, Biomedical Data Science MS, Business PhD, or Statistics Doctoral Minor Course Designation: Grad 50% - Counts toward 50% graduate coursework requirement Repeatable for Credit: No Last Taught: Spring 2026 Learning Outcomes: 1. Explain, evaluate, and avoid the ill-effects of finite-precision arithmetic in statistical calculations Audience: Graduate 2. Construct summary statistics from data using multiple algorithms, including best-practice approaches Audience: Graduate 3. Identify problems for which Monte Carlo simulation is appropriate, and deploy schemes to simulate random variables Audience: Graduate 4. Recognize statistical model fitting situations where tools from numerical linear algebra are required, and deploy various matrix decompositions for these situations Audience: Graduate 5. Demonstrate knowledge of basic convex analysis and how this is used to solve statistical optimization problems Audience: Graduate 6. Describe and deploy algorithmic strategies for both nonlinear and constrained optimization problems that arise in fitting statistical models Audience: Graduate 7. Construct confidence sets for a parameter, standard errors for an estimator, a p-value for a hypothesis test, or a prediction accuracy estimate for a predictor in both standard and non-standard statistical settings Audience: Graduate 8. Use graph-based approaches to deploy Bayesian posterior analysis Audience: Graduate 9. Design, deploy, and justify various Markov-chain Monte Carlo algorithms for statistical inference Audience: Graduate 10. Outline the structure of specialized optimization tools used in statistics Audience: Graduate 11. Deploy computations on a variety of data structures using R programming tools Audience: Graduate Learning Outcomes: 1. Explain, evaluate, and avoid the ill-effects of finite-precision arithmetic in statistical calculations Audience: Graduate 2. Construct summary statistics from data using multiple algorithms, including best-practice approaches Audience: Graduate 3. Identify problems for which Monte Carlo simulation is appropriate, and deploy schemes to simulate random variables Audience: Graduate 4. Recognize statistical model fitting situations where tools from numerical linear algebra are required, and deploy various matrix decompositions for these situations Audience: Graduate 5. Demonstrate knowledge of basic convex analysis and how this is used to solve statistical optimization problems Audience: Graduate 6. Describe and deploy algorithmic strategies for both nonlinear and constrained optimization problems that arise in fitting statistical models Audience: Graduate 7. Construct confidence sets for a parameter, standard errors for an estimator, a p-value for a hypothesis test, or a prediction accuracy estimate for a predictor in both standard and non-standard statistical settings Audience: Graduate 8. Use graph-based approaches to deploy Bayesian posterior analysis Audience: Graduate 9. Design, deploy, and justify various Markov-chain Monte Carlo algorithms for statistical inference Audience: Graduate 10. Outline the structure of specialized optimization tools used in statistics Audience: Graduate 11. Deploy computations on a variety of data structures using R programming tools Audience: Graduate