Directional Statistics for Innovative Applications: A Bicentennial Tribute to Florence Nightingale

Readership: Graduate students, researchers and practitioners interested in mathematical and applied statistics, especially directional data analytics and their applications to real-world problems.

This special volume is dedicated to the 200th birth anniversary of Florence Nightingale, OM, RRC, DStJ, (1820–1910), the Lady with the Lamp. As summarized in the preface, her contributions to Statistics include her detailed compilation of data to support her arguments for change in military hospitals, recognized as an important factor in the development of a positive image of Statistics as a science in its own right; her use of Rose diagrams to illustrate periodic data, one of the earliest instances of the analysis of circular data (with her pioneering efforts she may be acknowledged as the Lady with the Rose); and her efforts through nontrivial data collection and statistical presentations toward the improvement of health conditions and mortality rates. To celebrate the achievements, this volume is produced by two eminent editors Professors Ashis SenGupta and Barry Arnold, along with an outstanding group of 58 collaborative authors and 49 renowned reviewers from 25 countries.

This volume covers a wide range of topics in increasingly important directional statistics on exploratory data analysis, probability distributions on manifolds, maximum entropy, directional regression modeling, spatio-directional time series, optimal inference, statistical machine learning, simulation and computation, ranging from data on circles to that on spheres, tori and cylinders. It spans from recent theoretical development and promising methods to pioneering applications to evolving real-world problems in many areas such as astro-statistics, bioinformatics, crystallography, optimal transport, statistical process control and zoology.

This volume has eight parts to compile a total of 25 original research and review papers. It starts with the only paper in Part 1, Quality of Life in which Mukherjee concentrates on Florence Nightingale’s work related to public health and the connections to current research on quality of life.

Part 2, Innovative Applications has five papers. Mardia, Barber, Burdett, Kent, and Hamelryck use spherical mixture models in the context of protein folding problems. Arnold, Jupp, and Schaeben examine statistics associated with orientation relationships involving crystals and pairs of crystals. Hundrieser, Klatt, and Munk deal with issues related to optimal transport in the context of circular distributions and their inference issues. Di Marzo, Panzera, Fensore, and Taylor investigate an updated model for forecasting the movement of the magnetic North Pole. Ameijeiras-Alonso and Crujeiras discuss the use of flexible parametric families of circular distributions in the analysis of car accident data.

Part 3, Data Visualization, Simulation and Transformations contains two papers. Jammalamadaka and Terdik conduct simulation and visualization of spherical distributions in three dimensions, while Johnson proposes a parametric family of transformations and uses it to improve the fit of a von Mises model.

Part 4, Distribution Theory and Parametric Inference contains six papers. Bekker, Rad, Arashi, and Ley consider generalized asymmetric distributions on the circle and the torus, and compare them with the alternative models. Gatto uses maximum entropy ideas to examine the generalized von Mises spectral distribution in the analysis of stationary time series. Shimizu and Imoto construct distributions via products of cardioid densities to describe the chrematistics of asymmetry and multimodality. Abe, Imoto, Shiohama, and Miyata propose new circular, toroidal and cylindrical models, and address their inference and identifiability issues. Ong and SenGupta investigate bivariate cardioid distributions constructed using mixtures, as well as appropriate inference and tests of simplifying hypotheses. Kim and Asare-Kumi make inference and outlier detection for a three parameter generalized von Mises distribution to model asymmetric data.

Part 5, Regression Analysis includes four papers. Guttorp and Lockhart investigate how wind speed affects the parameters of a mixture of von Mises distributions. Lagona introduces autoregressive models for spatial circular data with parameters that are covariate dependent. Zhan, Ma, and Liu view circular data as unit complex numbers and propose a complex multiplication framework for circular regression. Jha and Biswas review a number of regression models for directional variables together with discussion of associated inferential and computational issues.

Part 6, Nonparametric Inference includes two papers. Chaubey reviews several smoothing methods for circular distributions and studies transformations to adapt linear algorithms in analyzing circular data. Verdebout implements the use of weighted sign tests for investigating and testing rotational symmetry against skewed alternatives.

Part 7, Time Series and Change-Point Analysis has three papers. Beran, Steffens, and Ghosh present results on circular time series exhibiting long range dependence. Ugwuowo discusses several circular time series models and illustrates their use in modeling wind direction data. Potgieter, Lombard, and Hawkins review statistical process control methodology in the context of circular data for identifying changes in location and/or concentration which may imply that a process is out of control.

Part 8, Statistical Machine Learning includes two papers. Laha and Majumdar consider neural network models for angular–angular and angular–linear regression. Tugac and Yildirak use deep learning algorithms and circular principal component analysis for forecasting multivariate wind data time series.

Overall, it is a remarkable contribution dedicated to Florence Nightingale which presents an extensive account of the latest research in directional statistics and their applications to various areas. It is a handy and powerful volume among the less than a dozen existing books in directional statistics.

Shuangzhe Liu
University of Canberra, Bruce, Australia
[email protected]