Essentials of Probability Models and Statistical Inference

3 units

This course provides a foundational yet comprehensive introduction to probability models and statistical inference, tailored for graduate students in data science. Students will learn to construct and apply probability models, explore various sampling strategies, and interpret statistical paradoxes, all within the broader context of modeling and drawing conclusions from data. The course emphasizes both theoretical understanding and methodological application, covering three core modules: (1) probability models, including the multivariate Gaussian distribution and exponential family distributions; (2) frequentist inference, including estimation, maximum likelihood estimation, consistency and efficiency, sufficiency, and the EM algorithm; and (3) Bayesian inference, covering prior and posterior distributions, conjugate priors, Bayesian risk, and computational methods such as MCMC. By integrating both frequentist and Bayesian perspectives, this course equips students with essential tools for statistical reasoning and data-driven decision making.