Statistical Computing for Data Analysis: Basic and advanced R programming; data management; spread sheets; verifying data accuracy; transferring data between software packages; data and graphical analysis with statistical software packages; algorithmic programming concepts and applications; simulation studies and resampling methods; software reliability; statistical modeling and machine learning.
Statistical Methods for Data Analysis: Principles of data analysis and scientific inference, including estimation, hypothesis testing, and the construction of interval estimates. Statistical concepts and models, including group comparison, blocking, and linear regression. Different sections are designed for students in various disciplines, and additional methods covered may depend on the target audience. Topics covered may include basic experimental designs and analysis of variance for those designs, analysis of categorical data, logistic and log-linear regression, likelihood-based inference, and the use of simulation.
Statistical Theory for Data Analysis: Introduction to the theoretical basis of fundamental statistical methods. Probability and probability distributions, moments and moment generating functions, conditional expectation, and transformation of random variables. Estimation based on loss functions, maximum likelihood, and properties of estimators. Sampling distributions, exact and asymptotic results, and the development of intervals. Principles of Bayesian analysis, inference from posterior distributions, and optimal prediction. Uses simulation to verify and extend theoretical results.
Experimental Design and Data Analysis: The role of statistics in research and the principles of experimental design. Concepts of experimental and observational units, randomization, replication, blocking, subdividing and repeatedly measuring experimental units; factorial treatment designs and confounding; common designs including randomized complete block design, Latin square design, split-plot design, and analysis of data from such common designs; extensions of the analysis of variance to cover variance components. Determining sample size.
Time Series Data Analysis: Methods for analyzing data collected over time; review of multiple regression analysis. Elementary forecasting methods: moving averages and exponential smoothing. Autoregressive-moving average (Box-Jenkins) models: identification, estimation, diagnostic checking, and forecasting. Transfer function models and intervention analysis. Introduction to multivariate time series methods.
Bayesian Data Analysis: Probability models and prior distributions; updating priors through the likelihood function. Computational and simulation-based methods for deriving posterior distributions and for estimating parameters. Basic statistical and hierarchical models. Model adequacy and posterior predictive checks. Markov Chain Monte Carlo methods and introduction to software for Bayesian data analysis.
Multivariate Data Analysis: Statistical and graphical methods for displaying and analyzing multivariate data; organizing and summarizing analyses of multivariate data; comparing two group mean vectors; multivariate analysis of variance; reducing variable dimension with principal components; identifying factors with exploratory factor analysis; grouping observations with multidimensional scaling and cluster analysis; classification.
Statistical Machine Learning and Artificial Intelligence: Introduction to machine learning and artificial intelligence concepts; training and test sets; assessment and diagnostics: overfitting, error rates, residual analysis, model assumptions checking, feature selection, variable importance; deep learning methods; transformers; generative artificial intelligence; ethical issues in machine learning and artificial intelligence; communicating findings to stakeholders in written, oral, visual and electronic form.
Principles of Statistical Consulting: Interacting with investigators to understand research goals and questions of interest; identifying data collection strategies and data analysis methods to address questions and goals; advising investigators on the appropriate use of statistical methods; ethical guidelines for statistical practice.
Experiential Learning in Applied Statistics: An internship or work experience that makes use of statistical methods featured in the Master of Applied Statistics degree program.