Core mathematical foundations of classical and Bayesian statistical inference. Theory of point and interval estimation and testing based on efficiency, consistency, sufficiency and robustness. Maximum likelihood, moments and non-parametric methods based on exact or large sample distribution theory; associated EM, asymptotic normality and bootstrap computational techniques. Theoretical aspects of objective Bayesian inference, prediction, and testing. Selected additional topics drawn from, for example, multiparameter testing, contingency tables, multiplicity studies.
Art and science of building graphical models and stochastic simulation methods for inference and prediction. Mixture models, networks, and other latent variable probability models, i.e. hidden Markov models. Review of discrete and continuous multivariate distributions used in building graphical models, tools of linear algebra and probability calculus. Aspects of Monte Carlo methodology and related dynamical modeling theory. Statistical computing using Matlab or R. Instructor consent required. Prerequisites: STA521L, STA523L, STA601. One course / 3 units.
Statistical programming, computation using selected languages and environments (Python, R, Matlab, and/or C/C++) and their interfaces with custom code development for central statistical models. Best practices and software development for reproducible results, selecting topics from: use of markup languages, understanding data structures, design of graphics, object oriented programming, vectorized code, scoping, documenting code, profiling and debugging, building modular code, and version control-all in contexts of specific applied statistical analyses. Designed to complement STA601.
Exploratory data analysis techniques and visualization of data with interactive graphics. Multiple linear regression and model building, predictive distributions, penalized and Bayesian estimation, model selection and model uncertainty including variable transformations, variable selection, and Bayesian model averaging, diagnostics and model checking, robust estimation, hierarchical models. Instructor consent required. Prerequisites: STA210, STA230 and STA250 or equivalents, STA601 (or co-registration). One course / 3 units.
Continuation of STA497S. Statistical and mathematical underpinnings of methodological research in statistical science. Student presentations of their statistical research in collaboration with, and under the supervision of, a DSS faculty mentor. Consent of department required. One course.
Statistical and mathematical underpinnings of methodological research in statistical science. Student presentations of their statistical research in collaboration with, and under the supervision of, a DSS faculty mentor. Offered only in fall semesters. Permission of department required. One course.
Data analysis, exploration, and representation. Scientific modeling and computation. Data mining for large datasets, algebraic decomposition methods, stochastic simulation for temporal models of dynamic processes, graphical and network data, computational methods development. Problems and data drawn from DSS research projects. Prerequisites: STA360 and some computer programming expertise. One course.
Immerses students into real world consulting, exposing them to all aspects of research including data collection, modeling, and evaluating results. Through campus-wide consulting program, students work with researchers from various disciplines providing recommendations for statistical methodologies appropriate for their research. Projects examined through lens of research ethics underlying data collection, model assumptions, analysis, reproducibility, and reporting of results.
Introduction to Bayesian modeling for data with spatial and/or time dependence. Exploratory analysis of spatial (point referenced and areal) and time series data. Gaussian processes and generalizations. Extending hierarchical Bayesian linear models and generalized linear models. Spatial models: CAR, SAR, kriging and time series models: ARM, ARMA, dynamic linear models. Computational methods for model fitting and diagnostics. Prerequisite: STA360, STA601 or equivalent. One course.
Students apply statistical analysis skills to in-depth data analysis projects ranging across diverse application areas including but not limited to energy, environmental sustainability, global health, information and culture, brain sciences, and social networks. Students practice cutting-edge statistical methods and communicate their results both technically and non-technically via presentations and written reports. Prerequisite: STA360 or instructor permission. One course.