flowchart TD C1["1. Probability"] --> C2["2. Markov chains"] C1 --> C3["3. The model"] C2 --> C3 C3 --> C4["4. Observation models"] C3 --> C5["5. Inference"] C4 --> C5 C5 --> C6["6. Estimation"] C5 --> C7["7. Computation"] C6 --> C7 C6 --> C8["8. Asymptotics"] C2 --> C8 C5 --> C9["9. Bayesian"] C9 --> C10["10. Hierarchical"] C9 --> C11["11. Telescoping"] C10 --> C11 C5 --> C12["12. State-space"] C5 --> C13["13. Online and decision"] C6 --> C14["14. Applications"] C10 --> C14 C14 --> C15["15. Exercises"]
Appendix B — Reading guide
Which chapters depend on which, and where to start depending on what you want.
B.1 Dependencies
Two dependencies worth flagging. Chapter 11 needs Chapter 9 for forward filtering with backward sampling and Dirichlet conjugacy, and benefits from Chapter 10 for the prior structure, but does not require Chapter 8. And Chapter 7 sits after Chapter 6 because it discusses the cost and the monotonicity check of EM, though its first half — underflow and scaling — can be read straight after Chapter 5.
B.2 Routes through the material
B.2.1 A first course on HMMs
Chapter 3, Chapter 4, Chapter 5, Chapter 6, Chapter 7.
Enough to specify a model, fit it, check it and interpret the output. Skip the measure-theoretic material in Chapter 1, referring back only for the KL divergence results used by EM. Follow with Chapter 14 for worked settings and the exercises marked (*) in Chapter 15.
B.2.2 Theory
Chapter 1, Chapter 2, Chapter 3, Chapter 5, Chapter 8.
A self-contained development from conditional expectation to asymptotic normality. Chapter 2 supplies the contraction results, Chapter 5 supplies filter stability, and Chapter 8 combines them. Read Cappé et al. (2005, chs. 12–13) in parallel.
B.2.3 Bayesian methods
Chapter 5 for the recursions, then Chapter 9, Chapter 10, Chapter 11.
Chapter 9 is the prerequisite for the other two. Someone interested only in the unknown-\(K\) problem can read Chapter 9 and Chapter 11 and skip Chapter 10, at the cost of missing the connection to the HDP-HMM.
B.2.4 Applied modelling
Chapter 3, Chapter 4, Chapter 5, Chapter 6, Chapter 7, Chapter 10, Chapter 14.
Weighted towards specification and diagnosis rather than proof. Chapter 10 is included because most applied problems involve several series rather than one, and the multilevel formulation is usually the right default.
B.3 A twelve-week course
The schedule at the end of Chapter 15 maps chapters to weeks and exercises. In outline: two weeks on foundations, two on the model, three on inference, estimation and computation, one on asymptotics, two on Bayesian and hierarchical methods, and two on extensions and applications.
Two adjustments are worth considering. If students are strong in probability, compress the first two weeks into one and spend the time on Chapter 11, which rewards a slow reading. If the course is applied, drop Chapter 8 to a single lecture and expand Chapter 14, using the animal movement examples in Zucchini et al. (2016, chs. 15–16), which are the best documented in the literature.
B.4 Prerequisites
Assumed: undergraduate probability, linear algebra through eigenvalues, calculus, and some exposure to likelihood-based inference.
Not assumed: measure theory, stochastic processes, Bayesian computation. Each is introduced where needed — measure-theoretic language in Chapter 1, Markov chain theory in Chapter 2, MCMC in Chapter 9.
Implementation exercises assume the ability to write a loop and call a linear algebra routine. Language is immaterial; the notes use no code.