Week 1: Discrete time Markov chains, Properties of Markov Processes

Week 2: Irreducibility, Recurrence and Transience, Invariant distribution

Week 3: Reversibility and detailed balance, Ergodicity

Week 4: Introduction and Inference in Hidden Markov Models,

Week 5: Filtering, prediction and smoothing

Week 6: Forward filtering Backward smoothing

Week 7: Exact inference infinite state-space HMMs

Week 8: Particle filters for optimal filtering in HMM

Week 9: Motivation for particle filters

Week 10: Particle filtering for HMM, Filtering, prediction, and smoothing densities

Week 11: Estimating the evidence

Week 12: Choice of the importance density Extensions to HMMs

Week 13: The Rao-Blackwellised particle filter.

Week 14: Wrap up