QS

Causal Inference

Statistical issues in causality and methods for estimating causal effects. Randomized designs and alternative designs and methods for when randomization is infeasible: matching methods, propensity scores, longitudinal treatments, regression discontinuity, instrumental variables, and principal stratification. Methods are motivated by examples from social sciences, policy and health sciences. Prerequisites: STA531, STA532, STA523L. One course / 3 units.

Statistical Decision Theory

Formulation of decision problems; criteria for optimality: maximum expected utility and minimax. Axiomatic foundations of expected utility; coherence and the axioms of probability (the Dutch Book theorem). Elicitation of probabilities and utilities. The value of information. Estimation and hypothesis testing as decision problems: risk, sufficiency, completeness and admissibility. Stein estimation. Bayes decision functions and their properties. Minimax analysis and improper priors. Decision theoretic Bayesian experimental design. Combining evidence and group decisions.

Statistical Data Mining

Introduction to data mining, including multivariate nonparametric regression, classification, and cluster analysis. Topics include the curse of dimensionality, the bootstrap, cross-validation, search (especially model selection), smoothing, the backfitting algorithm, and boosting. Emphasis on regression methods (e.g., neural networks, wavelets, the LASSO, and LARS), classifications methods (e.g., CART, Support vector machines, and nearest-neighbor methods), and cluster analysis (e.g., self-organizing maps, D-means clustering, and minimum spanning trees).

Introduction to Mathematical Statistics

Formal introduction to basic theory and methods of probability and statistics: probability and sample spaces, independence, conditional probability and Bayes’ theorem; random variables, distributions, moments and transformations. Parametric families of distributions and central limit theorem. Sampling distributions, traditional methods of estimation and hypothesis testing. Elements of likelihood and Bayesian inference. Basic discrete and continuous statistical models. Not open to students who have had STA250/MATH342. One course / 3 units.

Bayesian and Modern Statistics Analysis

Principles of data analysis and modern statistical modeling. Exploratory data analysis. Introduction to Bayesian inference, prior and posterior distributions, hierarchical models, model checking and selection, missing data, introduction to stochastic simulation by Markov Chain Monte Carlo using a higher level statistical language such as R or Matlab. Applications drawn from various disciplines. Not open to students with credit for STA360. Prerequisite: STA210, STA230 and STA250, or close equivalents, and STA611. One course.

Bayesian and Modern Statistical Data Analysis

Principles of data analysis and modern statistical modeling. Exploratory data analysis. Introduction to Bayesian inference, prior and posterior distributions, predictive distributions, hierarchical models, model checking and selection, missing data, introduction to stochastic simulation by Markov Chain Monte Carlo using a higher level statistical language such as R or Matlab. Applications drawn from various disciplines. Not open to students with credit for STA360. Prerequisite: STA210, STA230 and STA250, or close equivalents. One course / 3 units.

Probabilistic Machine Learning

Introduction to concepts in probabilistic machine learning with a focus on discriminative and hierarchical generative models. Topics include directed and undirected graphical models, kernel methods, exact and approximate parameter estimation methods, and structure learning. Prerequisites: Linear algebra, STA250 or STA611. One course / 3 units.

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