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STAT 471

INTRODUCTION TO COMPUTATIONAL STATISTICS

3 credits.

Classical statistical procedures arise where closed-form mathematical expressions are available for various inference summaries (e.g. linear regression; analysis of variance). A major emphasis of modern statistics is the development of inference principles in cases where both more complex data structures are involved and where more elaborate computations are required. Topics from numerical linear algebra, optimization, Monte Carlo (including Markov chain Monte Carlo), and graph theory are developed, especially as they relate to statistical inference (e.g., bootstrapping, permutation, Bayesian inference, EM algorithm, multivariate analysis).

Prerequisites & course information

Requisites: STAT/MATH 310 and ( STAT 333 or 340 ), graduate/professional standing, or declared in Statistics VISP Course Designation: Core GenEd - Natural Science & Wellness Breadth - Natural Science Level - Intermediate L&S Credit - L&S Liberal Arts and Science Repeatable for Credit: No Last Taught: Fall 2025 Learning Outcomes: 1. Use computational tools (alongside mathematical ones) to extract information from (a) the likelihood function, the central object of interest in frequentist statistics, and (b) the posterior distribution, the central object of interest in Bayesian statistics Audience: Undergraduate 2. Describe, understand the theoretical properties of, and implement basic algorithms for optimizing likelihood functions, including least squares and the IRLS algorithm, and the EM algorithm Audience: Undergraduate 3. Understand random numbers and pseudorandom numbers and how to distinguish them, and utilize a variety of techniques for generating random variates from a probability distribution Audience: Undergraduate 4. Use Monte Carlo methodology for such purposes as (a) carrying out a simulation study to study the properties of a statistical method, or (b) performing statistical inference via the bootstrap, or MCMC Audience: Undergraduate 5. Understand the use of graphical models for representing the structure of complex joint distributions, and be able to use computational tools to extract information from graphical models Audience: Undergraduate Learning Outcomes: 1. Use computational tools (alongside mathematical ones) to extract information from (a) the likelihood function, the central object of interest in frequentist statistics, and (b) the posterior distribution, the central object of interest in Bayesian statistics Audience: Undergraduate 2. Describe, understand the theoretical properties of, and implement basic algorithms for optimizing likelihood functions, including least squares and the IRLS algorithm, and the EM algorithm Audience: Undergraduate 3. Understand random numbers and pseudorandom numbers and how to distinguish them, and utilize a variety of techniques for generating random variates from a probability distribution Audience: Undergraduate 4. Use Monte Carlo methodology for such purposes as (a) carrying out a simulation study to study the properties of a statistical method, or (b) performing statistical inference via the bootstrap, or MCMC Audience: Undergraduate 5. Understand the use of graphical models for representing the structure of complex joint distributions, and be able to use computational tools to extract information from graphical models Audience: Undergraduate

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