Mathematics & Statistics

• CAS MA 576: Generalized Linear Models
  Undergraduate Prerequisites: (CASMA575) or consent of instructor. - Covers topics in linear models beyond MA 575: generalized linear models, analysis of binary and polytomous data, log-linear models, multivariate response models, non-linear models, graphical models, and relevant model selection techniques. Additional topics in modern regression as time allows.
• CAS MA 577: Mathematics of Financial Derivatives
  Undergraduate Prerequisites: (CASMA 581 or ENGEK 381 or ENGEK 500); or consent of instructor. - Develops the probabilistic tools used in finance and presents the methodologies that are used in the pricing of financial derivatives. No previous knowledge of finance is required.
• CAS MA 578: Bayesian Statistics
  Undergraduate Prerequisites: CASMA 575 or consent of instructor. - 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
  Undergraduate Prerequisites: (CASMA226 OR CASMA231) or equivalent, and elementary knowledge of linear algebra. - 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
  Undergraduate Prerequisites: (CASMA 225 OR CASMA 230 or CDSDS 122) or consent of instructor. - Graduate Prerequisites: (CASMA225 OR CASMA230) or consent of instructor. - 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 CASMA 381.
• CAS MA 582: Mathematical Statistics
  Undergraduate Prerequisites: : (CASMA 581 or ENGEK 381 or ENGEK 500) or consent of instructor. - 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
  Undergraduate Prerequisites: CASMA 581 or ENGEK 381 or ENGEK 500) or consent of instructor. - 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
  Undergraduate Prerequisites: CASMA 581 or ENGEK 381 or ENGEK 500 or consent of instructor. - 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 586: Stochastic Methods for Algorithms
  Undergraduate Prerequisites: First-Year Writing Seminar (e.g., WR 120); and (CASCS 111 or CDSDS 110, or ENGEK 125) and (CASMA 225 or CASCS 235 or CDSDS 122) and (CASMA 242 or CASMA 442 or CASCS 132 or CDSDS 121 or ENGEK 103) and (CASMA 581 or CASCS 237 or ENGEK 381 or ENGEK 500) or consent of instructor. - Application of stochastic process theory to design and analyze algorithms used in statistics and machine learning, especially Markov chain Monte Carlo and stochastic optimization methods. Emphasizes connecting theoretical results to practice through combination of proofs, numerical experiments, and expository writing. Effective Fall 2023, this course fulfills a single unit in each of the following BU Hub areas: Writing-Intensive Course, Creativity/Innovation.
  BU Hub Learn More

  • Creativity/Innovation
  • Writing-Intensive Course
• CAS MA 588: Nonparametric Statistics
  Undergraduate Prerequisites: CASMA 582 or consent of instructor. - 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
  Undergraduate Prerequisites: CASMA 575 or consent of instructor. - 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
  Undergraduate Prerequisites: CASMA 575 or consent of instructor. - 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.
• CAS MA 684: Applied Multiple Regression and Multivariable Methods
  Undergraduate Prerequisites: one year of statistics. - Graduate Prerequisites: one year of statistics. - Application of multivariate data analytic techniques. Multiple regression and correlation, confounding and interaction, variable selection, categorical predictors and outcomes, logistic regression, factor analysis, MANOVA, discriminant analysis, regression with longitudinal data, repeated measures, ANOVA.
• CAS MA 685: Advanced Topics in Applied Statistical Analysis
  Undergraduate Prerequisites: (CASMA684) or consent of instructor. - Graduate Prerequisites: (CASMA684) or consent of instructor. - Continues topics of CAS MA 684 at a more advanced level. Canonical correlation, multivariate analysis of variance, multivariate regressions. Categorical dependent variables techniques; discriminant analysis, logistic regression, log-linear analysis. Factor analysis; principal-axes, rotations, factor scores. Cluster analysis. Power analysis. Extensive use of statistical software.