Kai Li

Researcher and educator working in statistics, reinforcement learning, modeling, and simulation.

This page is part of my personal academic record, not an official course website.

Course description

Probability and distributions; multivariate distributions; distributions of functions of random variables; sampling distributions; limiting distributions; point estimation; confidence intervals; sufficient statistics; Bayesian estimation; maximum likelihood estimation; statistical tests.

Textbooks and resources

Required textbook

  • Statistical Inference by George Casella and Roger L. Berger, 2nd edition, 2002, Duxbury Advanced Series

Supplementary textbooks

  • Introduction to Mathematical Statistics by Robert Hogg, Joseph McKean and Allen Craig, 8th edition, 2018, Pearson
  • Mathematical Statistics and Data Analysis by John A. Rice, 3rd edition, 2006, Cengage
  • Introduction to Mathematical Statistics and Its Applications by Richard Larsen and Morris Marx, 6th edition, 2017, Pearson
  • John E. Freund’s Mathematical Statistics with Applications by Irwin Miller and Marylees Miller, 8th edition, 2018, Pearson

Learning outcomes

  1. Understand mathematical concepts on statistical methods in:
    • Probability and distributions;
    • Sampling;
    • Estimation;
    • Hypothesis testing.
  2. Demonstrate skills with solutions for basic statistical methods including:
    • Expectation, variance and moment generating functions for various distributions;
    • Consistency and Limiting distributions;
    • Bayesian methods;
    • Maximum likelihood methods, method of moments, empirical methods, random number generation, and other techniques.
  3. Understand mathematical properties of methods used in statistics:
    • Apply knowledge derived from the mathematical subjects including calculus, analysis, and linear algebra;
    • Provide a derivation for statistical formulas.
  4. Demonstrate the ability to follow, construct, and write mathematical proofs.
  5. Demonstrate understanding of how statistics is used in the solution of real-world problems.
  6. Demonstrate understanding of the assumptions, derivation of formulae, interpretation of results from statistical analysis.
  7. Understand the meaning of statistical theorems and formulas and their implications for real problems.
  8. Gain the ability to develop theories for statistical inference and testing for research on real-world problems.

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