Mathematics & Statistics

• CAS MA 578: Bayesian Statistics
  The principles and methods of Bayesian statistics. Subjective probability, Bayes rule, posterior distributions, predictive distributions. Computationally based inference using Monte Carlo integration, Markov chain simulation. Hierarchical models, mixture models, model checking, and methods for Bayesian model selection.
• CAS MA 579: Numerical Methods for Biological Sciences
  Introduction to the use of numerical methods for studying mathematical models of biological systems. Emphasis on the development of these methods; understanding their accuracy, performance, and stability; and their application to the study of biological systems.
• CAS MA 581: Probability
  Basic probability, conditional probability, independence. Discrete and continuous random variables, mean and variance, functions of random variables, moment generating function. Jointly distributed random variables, conditional distributions, independent random variables. Methods of transformations, law of large numbers, central limit theorem. Cannot be taken for credit in addition to CAS MA 381.
• CAS MA 582: Mathematical Statistics
  Point estimation including unbiasedness, efficiency, consistency, sufficiency, minimum variance unbiased estimator, Rao-Blackwell theorem, and Rao-Cramer inequality. Maximum likelihood and method of moment estimations; interval estimation; tests of hypothesis, uniformly most powerful tests, uniformly most powerful unbiased tests, likelihood ratio test, and chi-square test.
• CAS MA 583: Introduction to Stochastic Processes
  Basic concepts and techniques of stochastic process as they are most often used to construct models for a variety of problems of practical interest. Topics include Markov chains, Poisson process, birth and death processes, queuing theory, renewal processes, and reliability.
• CAS MA 585: Time Series and Forecasting
  Autocorrelation and partial autocorrelation functions; stationary and nonstationary processes; ARIMA and Seasonal ARIMA model identification, estimation, diagnostics, and forecasting. Modeling financial data via ARCH and GARCH models. Volatility estimation; additional topics, including long-range dependence and state-space models.
• CAS MA 588: Nonparametric Statistics
  The theory and logic in the development of nonparametric techniques including order statistics, tests based on runs, goodness of fit, rank-order (for location and scale), measures of association, analysis of variance, asymptotic relative efficiency.
• CAS MA 589: Computational Statistics
  Topics from computational statistics that are relevant to modern statistical applications: random number generation, sampling, Monte Carlo methods, computational inference, MCMC methods, graphical models, data partitioning, and bootstrapping. Emphasis on developing solid conceptual understanding of the methods through applications.
• CAS MA 592: Introduction to Causal Inference
  Concepts and methods for causal inference. You may have heard "association does not imply causation." But, what implies causation? In this course, we study how to estimate causal effects from data. We cover both experimental and non-experimental settings.

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