Hidden Markov Models for Time Series: An Introduction Using R, 2nd Edition, by Walter Zucchini, Iain L. MacDonald, and Roland Langrock
The second edition of Hidden Markov models for time series: an introduction using R, authored by Walter Zucchini, Iain L. MacDonald, and Roland Langrock, provides an excellent treatise about hidden Markov models (HMMs) and their applications. Because of the gentle conceptual and theoretical development, and the judicious provision of R code, this book will be very tractable to those looking for an introduction to the topic of HMMs with the intent of using them as soon as possible, as well as those wanting to review or expand their existing theoretical understanding. I anticipate that this book will occupy an important place in my collection, and indeed have already had the opportunity to use it in several research projects. I would recommend this book in particular to quantitative and statistical ecologists, biometricians, and statisticians.
This book spans a considerable wealth of material related to HMMs, including their basic structure and inferential approaches (Part 1), extensions to the basic HMM that illuminate the considerable breadth of conceptual models this framework can encompass (Part 2), and concluding with a collection of examples (Part 3). Terms are defined clearly, and contextual justification is amply provided throughout. Along with the inclusion of remarks and discussion material, and chapter introductions that often remind the reader the constraints of assumptions in previous material, together make this book an excellent resource.
Part 1 gives an overview of the components, theory, and estimation of HMMs. Chapters 1–2 provide the needed material on mixture and Markov models which together make up an HMM. This section also includes material on estimation approaches, and it is nice to see direct maximum likelihood and expectation maximization approaches described (Chapters 3–4) in some detail here in one place, while still being tractable. Bayesian inference of HMMs is also given some attention in Chapter 7. Importantly, beyond just the first step in statistical inference of model fitting, some techniques in model selection and checking are covered in Chapter 6, giving the reader some reference on these important steps. Chapter 8 concludes Part 1 with a brief review of some of the packages in R that focus on HMMs. It might be argued that the particular HMM (particular in the use of a Poisson distribution for the state-dependent distribution) used in Part 1 that is called the ‘basic model’ is a bit arbitrary, but this is no real substantive flaw in the book.
Part 2 describes several extensions to the basic HMM, which was introduced as one in which the observations follow a Poisson distribution conditional on the latent state. As indicated in the preface, Part 2 constitutes the major change in this second edition. The first of the extensions point out that the many observation distributions other than Poisson can be implemented (Chapter 9). Discussion of how covariates can be incorporated into the observation and state-transition probability dependencies is given in Chapter 10. This space commitment is well worth it in my opinion because incorporating covariates into the state-transition probabilities provides a direct way to incorporate pertinent covariate information into the Markov process, which is often where the science/hypothesis appears in an HMM. Chapter 11 addresses the notion that the latent states need not be finite or discrete. Here is where HMMs are seen as a special case of state-space models. While I value keeping a distinction between HMMs and state-space models, my preference would have been for this relationship to be introduced earlier, although it could be argued that making this realization is not germane to the development and application of HMMs as a stand alone modeling framework. The remaining two chapters in this part cover hidden semi-Markov models (Chapter 12) and longitudinal data analysis using HMMs (Chapter 13). Like the rest of this book, these chapters are well written while giving insight into fairly complicated formulations of HMMs that are nevertheless important to know about given the complexity of real-world data and models.
Part 3 and Appendix A gives a collection of examples and R code, mostly from the ecological and environmental sciences. These examples nicely cover many of the extensions to HMMs that real-world data analysis will require. The code provided will be especially valuable for making precise and correct application as easy as possible.
There are a number of exercises in many of the chapters, and a short Appendix B that provides proofs of some of the technical material.