Ley C., Verdebout T. Applied Directional Statistics Modern Methods and Case Studies

Boca Raton: CRC Press, 2019. — 317 p.This book collects important advances in methodology and data analysis for directional statistics. It is the companion book of the more theoretical treatment presented in Modern Directional Statistics (CRC Press, 2017). The field of directional statistics has received a lot of attention due to demands from disciplines such as life sciences or machine learning, the availability of massive data sets requiring adapted statistical techniques, and technological advances. This book covers important progress in bioinformatics, biology, astrophysics, oceanography, environmental sciences, earth sciences, machine learning and social sciences.Protein Structure
Protein Geometry
Structure Determination and Prediction
Markov Chain Monte Carlo Simulations of Proteins
Generative Models for the Polypeptide Backbone
Histograms and Fourier Series
A Dynamical Bayesian Network Model: TorusDBN
Generative Models for Amino Acids Side Chains
Discussion
Ambiguous Rotations
Symmetry Groups
Symmetric Frames
From Symmetric Frames to Symmetric Arrays
Summary Statistics
Testing Uniformity
A General Class of Distributions on SO(3)=K
Concentrated Distributions
One-Sample Tests
Further Developments
Analysis of Example
Correlated Cylindrical Data
Correlated Cylindrical Data
Modeling a Cylindrical Time Series
Modeling a Cylindrical Spatial Series
Identification of Sea Regimes
Segmentation of Current FieldsToroidal Diffusions and Protein Structure Evolution
Protein Structure
Protein Evolution
Toward a Generative Model of Protein Evolution
Toroidal Diffusions
Toroidal Ornstein-Uhlenbeck Analogues
Estimation for Toroidal Diffusions
Empirical Performance
Hidden Markov Model Structure
Site-Classes: Constant Evolution and Jump Events
Model Training
Benchmarks
Case Study: Detection of a Novel Evolutionary MotifSome Preliminaries about Harmonic Analysis on SO(3) and S2
Null and Alternative Hypotheses
Noise Assumptions
Test Constructions
The Testing Procedures
Alternatives
Simulations
Real Data: Paleomagnetism
Real Data: UHECRA Geometric Construction of the One Axis Model
Modeling Data from SE(3) and B3
The Rotation Only Estimator of the Rotation Axis A
The Translation Only Estimator of the Parameters
The Rotation-Translation Estimator of the Parameters
Simulations
Data Analysis
Discussion
Spatial and Spatio-Temporal Circular Processes with Application to Wave DirectionsThe Wrapped Spatial and Spatio-Temporal Process
Wrapped Spatial Gaussian Process
Kriging and Forecasting
Wave Data for the Examples
Wrapped Skewed Gaussian Process
Space-Time Analysis Using the Wrapped Skewed Gaussian Process
Univariate Projected Normal Distribution
Projected Gaussian Spatial Processes
Model Fitting and Inference
Kriging with the Projected Gaussian Processes
An Example Using the Projected Gaussian Process
A Separable Space-Time Wave Direction Data Example
Space-Time Comparison of the WN and PN Models
Joint Modeling of Wave Height and Direction
Concluding Remarks
Cylindrical Distributions and Their Applications to Biological DataProbability Distributions on [0;1)
Circular Distributions
The Johnson-Wehrly Distribution
The Weibull-von Mises Distribution
Gamma-von Mises Distribution
Generalized Gamma-von Mises Distribution
Sine-Skewed Weibull-von-Mises Distribution
Application : Quantification of the Speed/Turning Angle Patterns of a Flying Bird
Application of Cylindrical Distributions : How Trees Are Expanding Crowns
Crown Asymmetry in Boreal Forests
Crown Asymmetry Model
Results of the Cylindrical Models
Concluding Remarks
Introduction to Wildre modeling
Fires' Seasonality
Landscape Scale
Global Scale
Fires' Orientation
Main Spread on the Orientation of Fires
Orientation-Size Joint Distribution
Orientation-Size Regression Modeling
Open Problems
Bayesian Analysis of Circular Data in Social and Behavioral SciencesIntroducing Two Approaches Conceptually
Intrinsic
Embedding
Bayesian Modeling
Intrinsic
The Data
Bayesian Inference
Inequality Constrained Hypotheses
Basic Human Values in the European Social Survey
The Data
The Model
Variable Selection
Bayesian Inference
Comparison of Approaches
Discussion
Nonparametric Classification for Circular Data
Density Estimation on the Circle
Classification via Density Estimation
Binary Regression via Density Estimation
Local Polynomial Binary Regression
Numerical Examples
Classification of Earth's SurfaceUniform Distribution
Watson Distribution
Other Distributions
Modeling Directional Data: Maximum-Likelihood Estimation
Maximum-Likelihood Estimation for vMF
Maximum-Likelihood Estimation for Watson
Mixture Models
EM Algorithm
Limiting Versions
Application: Clustering Using movMF
Application: Clustering Using moWThe Circular Package
Packages that Use the Circular Package
The Directional Package
Other Packages for Directional Statistics
Unsupported Directional Statistics Methodologies