Open course material I have written in statistics and programming. Each course is a full, self-contained website with rendered mathematics, worked examples, and code.
Bayesian Statistics and Inference
A measure-theoretic, decision-theoretic treatment of Bayesian inference
Derives the major algorithms from first principles, with rigorous proofs of correctness and convergence, posterior analysis (propriety, consistency, identifiability), and both Bayesian and frequentist evaluation perspectives.
- Foundations & conjugate models Exact inference, regression, GLMs
- MCMC theory Metropolis–Hastings, Gibbs, advanced methods
- Approximate inference Variational inference, Gaussian processes
- Theory & criticism Asymptotics, consistency, model checking
A rigorous, mathematically heavy course on hidden Markov models
Built up from measure-theoretic probability through inference, estimation theory, and modern variants — proofs and derivations rather than code snippets, with proof-based problem sets throughout.
- Foundations Markov chains, stochastic matrices, spectral theory
- Inference algorithms Forward–backward, Viterbi, filtering, smoothing
- Estimation Maximum likelihood, EM / Baum–Welch, identifiability
- Advanced theory Asymptotics, continuous states, Kalman filter
- Applications Speech, bioinformatics, finance, epidemiology
R Programming: From Beginner to Expert
A practical R course from core syntax to professional workflows
Covers data analysis, statistical modelling, and reproducible practice in R and RStudio. Written for undergraduate and postgraduate students.
- Beginner to expert R Syntax, data structures, control flow
- Modelling & ML Data manipulation, statistics, machine learning
- Shiny applications Interactive web apps in R
- Developer tools Packages, testing, debugging, code organisation
- Time series case study Analysis and forecasting with Air Passengers