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Special Topics in Statistics

Course Title: Advanced Time Series Analysis

Course Description: This course will be a basic graduate course in time series analysis appropriate for PhD students and advanced Master's students in the Department of Statistics. It may also be appropriate for graduate students from other departments who have strong quantitative backgrounds and have met the necessary prerequisites. The course will include a balance of theory and applications that will give students sufficient preparation to analyze dependent data and to implement traditional time series methodology and appropriate extensions computationally.
The prerequisites for the course will be mathematical statistics (STAT 415 or 514), regression (STAT 511 or 501 or 462), and substantial background in linear algebra.

Course Title: Advanced Topics in Machine Learning

Course Description: Three advanced topics in machine learning are covered in this short course. The first topic is unsupervised clustering of high dimensional data, emphasizing clustering based on latent state graph models and geometric characteristics of density functions. The second topic is on optimal transport and its applications in machine learning. The third topic is explainable machine learning. R Cran packages will be introduced for high dimensional clustering, high dimensional density estimation, ensemble clustering, and uncertainty assessment for clustering. Students are encouraged to survey emerging topics in machine learning topics and to explore theory, methods, and practice for enhancing connections between statistics and machine learning.

  • Prerequisites: STAT557 or similar.
  • Instructor: Jia Li
  • Offered: Fall 2024

Course Title: Missing Data

Course Description: Most data analyses involve missing data in some capacity.  Even when the collected data are complete, questions regarding data collection, measurement error, or causal effects all involve data that might have been collected but were not.  This course will provide a framework for thinking about and working with missing data. Topics include the classification of ignorable and nonignorable data collection mechanisms, multiple imputation, data coarsening, and modern semiparametric estimation techniques.  Throughout, connections will be made to other areas of statistical practice, including surveys, censoring, and causal inference.  

  • Prerequisites: STAT 514 or similar.
  • Instructor: Cory McCartan
  • Offered: Fall 2024

Course Title: Statistical Approaches to Mechanistic Models

Course Description: In this class, we consider methods for statistical inference on parameters governing mechanistic models, including differential equation models. Class topics include an introduction to modeling with ordinary differential equations (ODEs) and stochastic differential equations (SDEs), numerical methods for solving systems of differential equations, standard approaches for statistical inference, simulation-based inference using particle filters, and emulation-based inference.

Course Title: Topics in Neuroimaging Data Analysis: A Big Data Paradigm

Course Description: In this course we will explore topics in the statistical analysis of neuroimaging data, such as functional magnetic resonance imaging (fMRI) and electroencephalogram (EEG). Students will learn about how the data are collected, their characteristics, and common statistical analysis approaches. Along the way, we will explore common themes in Big Data analysis that span neuroimaging, as well as other data types.

Course Title: Topics in Causal Modeling, Inference, and Reasoning

Course Description: A survey of causal inference models and methods with a focus on contemporary research areas. Topics include the potential outcomes framework, structural equation models, instrumental variable techniques, conditional independence tests and causal discovery methods, counterfactual estimation, and modern machine learning techniques.

Course Title: Introduction to Philosophy of Statistics

Course Description: Statistical reasoning is at the heart of science, and is becoming even more important as our data sets and research questions become more complex. This seminar course will provide an introduction to some key statistical ideas, relying on well known texts from H. Jeffreys, L.J. Savage, and M. DeGroot, among others. The course is targeted at graduate students in statistics but is open to students who have a background in probability and mathematical statistics. In addition to readings and class participation, students will be expected to write a research paper and prepare a class presentation.