Jabir Hussain
Course Notes
- Week 1 — Foundations: linear algebra + uncertainty propagation
- Week 2 — Least squares meets probability: normal equations + multivariate distributions
- Week 3 — Gaussian calculus + quadrature under the curse of dimensionality
- Week 4 — Monte Carlo toolkit: LLN, vanilla MC, MCMC, and Kalman filtering
- Week 5 — From MCMC convergence to infinite-dimensional structure: Hilbert spaces & operators
- Week 6 — Kernels and RKHS: approximation geometry + random-function basics
- Week 7 — Random functions in full: covariance operators, stochastic processes, and KL expansions
- Week 8 — Regression and inverse problems: pseudoinverses + regularisation as optimisation
- Week 9 — Regularisation deep dive + Bayesian inverse problems (linear Gaussian case)
- Week 10 — Gaussian processes + well-posed Bayesian inversion in high/infinite dimensions