Courses recently taught

MATH 608 Statistical Data Science

Prerequisites: A calculus-based statistics course (e.g., Math 628 or Math 526) and a linear algebra course (Math 290 or Math 291). Recommended: EECS 138 or equivalent experience.

Implementation: Python and Scikit-learn.

  • Linear regression and linear classification for high-dimensional problems
  • Support vector machines
  • Bayesian learning and the EM algorithm
  • Monte Carlo methods
  • Data augmentation
  • Probabilistic graphical models, undirected graphical models for continuous and discrete variables
MATH 611 Time Series Analysis

Prerequisites: A calculus-based statistics course (e.g., Math 628 or Math 526) and a linear algebra course (Math 290 or Math 291).

Implementation: Python and Statsmodels.

  • Modeling time series, trend, seasonality and residual process
  • Autocovariance function, multivariate time series, moving average and autoregression
  • Stationary processes, linear processes, linear filtering
  • Confidence intervals for the mean and the autocorrelation, hypothesis tests for a time series model
  • ARMA models, partial autocorrelation function, parameter estimation methods, forecasting, model selection
  • Stationary processes in the frequency domain, spectral density, periodogram, smoothing, spectral window
  • Nonstationary time series, ARIMA models
  • State-space representation, Kalman recursions
  • Recurrent neural networks as time allows
MATH 627 Probability

Prerequisites: Calculus III (Math 127 or Math 147) and Linear Algebra (Math 290 or Math 291).

  • Probability
  • Random variable, distribution, expectation
  • Discrete distributions
  • Continuous distributions
  • Random vector, multivariate distribution
  • Central limit theorem
MATH 728 Statistical Theory

Prerequisites: Math 727 Probability Theory.

  • Order statistics
  • Unbiasedness, consistency, limiting distribution
  • Method of moments, maximum likelihood estimation
  • Fisher information, Cramer-Rao lower bound, efficient estimator
  • Sufficient statistic, Blackwell-Rao theorem
  • Uniformly minimum variance unbiased estimator, Lehmann-Scheffe theorem
  • Optimal tests of hypotheses, uniformly most powerful test
  • Bayes estimation
MATH 874 Statistical Decision Theory

Prerequisites: A calculus-based probability course (e.g., Math 627 or Math 526) and a linear algebra course (e.g., Math 290 or Math 291). Recommended: statistics (e.g., Math 628 or Math 526) and knowledge of a programming language (e.g., EECS 138).

Implementation: PyTorch and Pyro-ppl.