Reviewof Books and Teaching Materials

Abstract

Applied Directional Statistics: Modern Methods and Case Studies is a great book on directional data analysis. It contains several interesting case studies and a number of useful statistical methods. The book consists of 13 chapters and each chapter is an independent paper covering various topics in directional statistics. This book provides a wide variety of different types of directional data. Data in this book can be roughly divided into three primary types. The first type comes from the angular difference between two arms/axes (Chapters 1, 4, and 9). A common scenario of this type is the protein folding problem where the each observation is the angular difference between two chemical bonds. The second type of direction data is from a measurement of directions (Chapters 3, 7, and 8). Chapters 3 and 7 both consider observations associated with orientation of waves in the ocean. In this case, the directional data are a univariate number representing the orientation of sea wave at a particular location. The third type is the measurement on a sphere (Chapters 5 and 11). In both Chapters 5 and 11, the directional data are measurements on the Earth so each observation represents a coordinate. In addition, this book also provides examples of directional data from other scenarios. Chapter 9 reparameterizes the seasonality using a direction, so each date in a year is represented as a particular angle on a sphere. This reparameterization provides a new insight into studying seasonal effects. Also, in Chapter 10, the authors describe two novel types of directional data. The first one is from a study of the development of spatial cognition of infants and the directional data represents the error in terms of a prediction of an angle (direction). In the same chapter, the authors also showcase another type of directional data from the Basic Human Value in the European Social Survey. In theses data, a univariate direction represents the position on a circumplex of two dimensions: openness to change versus conservative and self-enhancement versus self-transcendence. This book also discusses several modern methodologies for analyzing directional data. Chapters in this book can be roughly divided into three sets of methodologies. The first one is the set of parametric models (Chapters 6, 8, 10, and 12). These chapters discuss how to fit a wide variety of parametric models to a directional data and discuss the associated computational issues. The second set of methods consists of nonparametric techniques (Chapters 5, 9, and 11). In Chapter 5, the authors describe how to use orthonormal basis (spherical harmonics) to a 2D directional data. In Chapters 9 and 11, the authors study the idea of kernel smoothing in directional data and discuss various statistical tasks such as density estimation, regression, and classification. The third set of methods is dynamical modeling strategy (Chapters 1, 3, 4, and 7). Chapters 1, 3, and 4 study how to use hidden Markov models to jointly model directional data with temporal information. Chapters 4 and 7 discuss how to use a stochastic process procedure to handle a directional data that evolves over time. In addition to these methods, Chapter 2 studies the problem of hypothesis testing of directional data and provide methods for uniformity test and one/two-sample tests. Chapter 13 is a special chapter summarizing a collection of popular R packages of analyzing directional data. I would recommend Applied Directional Statistics to anyone who has a received graduate-level training in statistics and is interested in directional data. This book provides a wide variety of data examples that broadens readers’ horizon on the applicability of directional data. The methods described in this book are easy to follow and they all have connections with similar methods in Euclidean data. For instance, the directional kernel density estimator in Chapter 9 and 11 is closely related to the usual kernel density estimator in Euclidean space. These chapters serve as good reading references of a regular statistics course.