About This HMM Course

About the Hidden Markov Models (HMMs) Course

This site presents a rigorous, proof-oriented course on Hidden Markov Models (HMMs). It is designed for:

Graduate students in statistics, machine learning, or applied mathematics
Researchers and advanced practitioners who want a mathematically honest treatment of HMMs
Instructors who need a reference set of lecture-style notes and problem sets

The course emphasizes calm clarity over flash: clean typography, high-contrast math, and a modular layout so you can move between foundations, algorithms, theory, and applications without friction.

Pedagogical Philosophy

Theory-first, but example-driven. Core results are stated and proved, with pointers to Zucchini et al. and more advanced monographs.
Separation of concerns.
- Section 0–1: probability and Markov chains
- Section 2–3: model construction and likelihoods
- Section 4–5: algorithms and estimation
- Section 6–9: asymptotic theory and advanced variants
- Section 10–11: applications and proof-based problem sets
Notation stability. Notation is aligned as much as possible with Zucchini, MacDonald & Langrock to make cross-reading easy.

Who Should Use This Material

You will benefit most if you:

Are comfortable with undergraduate probability and linear algebra
Are willing to engage with proofs and derivations (not just code)
Want to connect HMM algorithms to broader ideas in stochastic processes and statistical inference

If your background is lighter, start with Section 0 (Mathematical Prerequisites) and use the references to fill any gaps.

How This Site Is Structured

Home page: Quick overview, value proposition, and module view of the course.
Overview (HMM.md): A textual syllabus with references and links to all sections.
Sections 0–11: Each section is a self-contained set of notes with definitions, theorems, and proof sketches.
Resources & Help:
- About (this page): context and intended audience
- FAQ: practical questions on using the notes
- Contact: how to suggest corrections or improvements

Primary References

This course is intentionally compatible with:

Zucchini, MacDonald, Langrock – Hidden Markov Models for Time Series: An Introduction Using R.
Cappé, Moulines, Rydén – Inference in Hidden Markov Models.
Douc, Moulines, Stoffer – Nonlinear Time Series: Theory, Methods and Applications.
Rabiner (1989) – A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition.

You can treat these notes as a bridge between the applied style of Zucchini et al. and the more measure-theoretic style of Cappé–Moulines–Rydén.

--- title: "About This HMM Course" number-sections: false --- # About the Hidden Markov Models (HMMs) Course This site presents a **rigorous, proof-oriented course on Hidden Markov Models (HMMs)**. It is designed for: - Graduate students in statistics, machine learning, or applied mathematics - Researchers and advanced practitioners who want a mathematically honest treatment of HMMs - Instructors who need a reference set of lecture-style notes and problem sets The course emphasizes **calm clarity** over flash: clean typography, high-contrast math, and a modular layout so you can move between foundations, algorithms, theory, and applications without friction. ## Pedagogical Philosophy - **Theory-first, but example-driven.** Core results are stated and proved, with pointers to Zucchini et al. and more advanced monographs. - **Separation of concerns.** - Section 0–1: probability and Markov chains - Section 2–3: model construction and likelihoods - Section 4–5: algorithms and estimation - Section 6–9: asymptotic theory and advanced variants - Section 10–11: applications and proof-based problem sets - **Notation stability.** Notation is aligned as much as possible with Zucchini, MacDonald & Langrock to make cross-reading easy. ## Who Should Use This Material You will benefit most if you: - Are comfortable with undergraduate probability and linear algebra - Are willing to engage with proofs and derivations (not just code) - Want to connect HMM algorithms to broader ideas in stochastic processes and statistical inference If your background is lighter, start with **Section 0 (Mathematical Prerequisites)** and use the references to fill any gaps. ## How This Site Is Structured - **Home page:** Quick overview, value proposition, and module view of the course. - **Overview (HMM.md):** A textual syllabus with references and links to all sections. - **Sections 0–11:** Each section is a self-contained set of notes with definitions, theorems, and proof sketches. - **Resources & Help:** - `About` (this page): context and intended audience - `FAQ`: practical questions on using the notes - `Contact`: how to suggest corrections or improvements ## Primary References This course is intentionally compatible with: - Zucchini, MacDonald, Langrock – *Hidden Markov Models for Time Series: An Introduction Using R*. - Cappé, Moulines, Rydén – *Inference in Hidden Markov Models*. - Douc, Moulines, Stoffer – *Nonlinear Time Series: Theory, Methods and Applications*. - Rabiner (1989) – *A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition*. You can treat these notes as a **bridge** between the applied style of Zucchini et al. and the more measure-theoretic style of Cappé–Moulines–Rydén.