This website contains the teaching materials that I create for DSA5209 Stochastic Methods and Inferences for Big Data in AY25/26 Semester 2 (Jan-Apr 2026). This is the first time that the course is taught at NUS, and I sincerely welcome comments and suggestions on these materials, especially since I am far from an expert in some, if not all of the contents.
I would like to credit the following excellent sources that helped me prepare these slides. Thank you, authors, I have learned so much from you, and you enabled me to convey my understanding of these contents to my dear students. If there are any copyright concerns, please contact me directly.
Larry Wasserman, All of Statistics
Andrew Gelman, John Carlin, Hal Stern, David Dunson, Aki Vehtari, and Donald Rubin, Bayesian Data Analysis
Daniel Sanz-Alonso and Omar Al-Ghattas, A First Course in Monte Carlo Methods
Lecture Notes on Markov Chains by Nicolas Privault (Singaporean Local!)
Course website of 21-387 Monte Carlo Methods and Applications at CMU, taught by Keenan Crane and Gautam Iyer
Harold Kushner and George Yin, Stochastic Approximation and Recursive Algorithms and Applications
Lecture Notes on Expectation Maximization by Hemant Tagare (there are many lecture notes on EM on the internet, you can learn from any one of them)
Mehryar Mohri, Afshin Rostamizadeh and Ameet Talwalkar, Foundations of Machine Learning
Kevin Murphy, Machine Learning: a Probabilistic Perspective
... and others... Contact me if I seem to forget to cite something
Slides: Lecture 1 Probability Review,
Lecture 2 Frequentist Estimators
Lecture 3 Frequentist Uncertainty Quantification
Lecture 4 Bayesian Inference I
Lecture 5 Bayesian Inference II
Lecture 6 Basics of Markov Chains
Lecture 7 Transformation & Rejection Sampling
Lecture 8 Importance Sampling, Variance Reduction and Metropolis-Hastings
Lecture 9 More on Metropolis-Hastings and Gibbs Samplers