SML 505 — Modern Statistics

The course provides an introduction to modern statistics and data analysis. It addresses the question, “What should I do if these are my data and this is what I want to know”? The course adopts a model based, largely Bayesian, approach. It introduces the computational means and software packages to explore data and infer underlying parameters from them. An emphasis will be put on streamlining model specification and evaluation by leveraging probabilistic programming frameworks. The topics are exemplified by real-world applications drawn from across the sciences.

Weekly Syllabus

  1. Principled Data Analysis: signal model and error model, likelihood and priors
  2. Probability Distributions
  3. Generative Clustering and Classification
  4. Gaussian Processes
  5. Fitting your own model: gradient-based optimization
  6. Automatic differentiation
  7. Error Estimation
  8. Sampling Methods: MCMC and variants
  9. Advanced Sampling: Hamiltonian MC, ensemble and nested methods
  10. Hierarchical Models
  11. Likelihood-free Methods
  12. Hypothesis testing

Reading

Lecture notes with code examples will be made available online.

Recommended Reading: