Teaching

Courses I have taught or helped teach, with the topics covered in each.

NUS · ST5201

Statistical Foundations of Data Science

  1. Probability
  2. Random Variables
  3. Joint Distributions
  4. Expected Values
  5. Limit Theorems
  6. Parameter Estimation
  7. Hypothesis Testing
  8. Sign Test
  9. Signed Rank Test
  10. Rank Sum Test

Cambridge

Statistics IB

  1. Introduction and probability revision
  2. Estimation, bias and mean squared error
  3. Sufficiency
  4. Maximum Likelihood Estimator (MLE)
  5. Confidence Intervals
  6. Bayesian estimation
  7. Simple Hypotheses
  8. Composite hypotheses
  9. Tests of goodness-of-fit and independence
  10. Tests in contingency tables
  11. Multivariate normal theory
  12. The linear model
  13. The normal linear model
  14. Inference in the normal linear model
  15. Special cases of the linear model
  16. Hypothesis testing in the linear model

Cambridge

Principles of Statistics

  1. Course overview
  2. Fisher information
  3. Cramér–Rao bound
  4. Stochastic convergence
  5. Central limit theorem
  6. Consistency of the MLE
  7. Asymptotic normality of MLE
  8. Plug-in MLE and Delta method
  9. Asymptotic inference with MLE
  10. Introduction to Bayesian statistics
  11. Between prior and posterior
  12. Frequentist analysis of Bayesian methods
  13. Decision theory & Bayesian risk
  14. Minimax risk and admissibility
  15. Admissibility in the Gaussian model
  16. Risk of the James–Stein estimator
  17. Classification problems
  18. Multivariate analysis
  19. Principal component analysis
  20. Resampling principles & the bootstrap
  21. Validity of the bootstrap
  22. Monte Carlo methods
  23. Markov chain Monte Carlo methods
  24. Introduction to nonparametric statistics

Cambridge

Mathematics of Machine Learning

  1. Review of conditional expectation
  2. Empirical risk minimisation
  3. Sub-Gaussianity and Hoeffding’s inequality
  4. Finite hypothesis classes
  5. Bounded difference inequality
  6. Rademacher complexity
  7. VC dimension
  8. Convex analysis
  9. Convex surrogates
  10. Rademacher complexity revisited
  11. Gradient descent
  12. Stochastic gradient descent
  13. Cross-validation
  14. Adaboost & Gradient boosting
  15. Decision trees & Random forests
  16. Feedforward neural networks