Over the last decade, statisticians have developed new statistical tools in the field of spatial point processes. At the same time, observational efforts have yielded a huge amount of new cosmological data to analyze. Although the main tools in astronomy for comparing theoretical results with observation are statistical, in recent years, cosmologists have not been generally aware of the developments in statistics and vice versa.
Statistics of the Galaxy Distribution describes both the available observational data on the distribution of galaxies and the applications of spatial statistics in cosmology. It gives a detailed derivation of the statistical methods used to study the galaxy distribution and the cosmological physics needed to formulate the statistical models. Because the prevalent approach in cosmological statistics has been frequentist, the authors focus on the most widely used of these methods, but they also explore Bayesian techniques that have become popular in large-scale structure studies.
Describing the most popular methods, their latest applications, and the necessary mathematical and astrophysical background, this groundbreaking book presents the state of the art in the statistical description of the large-scale structure of the Universe.
Cosmology's well-defined and growing data sets represent an important challenge for the statistical analysis, and therefore for the statistics community. Statistics of the Galaxy Distribution presents a unique opportunity for researchers in both fields to strengthen the connection between them and, using a common language, explore the statistical description of the universe.
Table of Contents
THE CLUMPY UNIVERSE
Mapping the Universe
Selection Effects and Biases
Current and Future Galaxy Catalogs
The Observed Structures: Clusters, Filaments, Walls and Voids
THE STANDARD MODEL OF THE UNIVERSE
The Friedmann-Robertson-Walker Universe
Basic Observational Data
COSMOLOGICAL POINT PROCESSES
The Relation Between Discrete and Continuous Distributions
The Two-Point Correlation Function
N-Point Correlation Functions
Moments and Counts in Cells
The Void Probability Function
Nearest Neighbor Distances
Galaxy Distribution as a Marked Point Field
FRACTAL PROPERTIES OF THE GALAXY DISTRIBUTION
Fractal Models for the Universe
Tests on Projected Data
STATISTICAL AND GEOMETRICAL MODELS
The Neyman-Scott Process and Related Models
The Voronoi Model
Statistical Models for the Counts in Cells
FORMATION OF STRUCTURE
Dynamics of Structure
The Linear Approximation
RANDOM FIELDS IN COSMOLOGY
Gaussian Random Fields
Realizations of Random Fields
Statistics of Peaks in Gaussian Random Fields
Halo Model of Galaxy Clustering
Stochastic and Nonlinear Biasing
FOURIER ANALYSIS OF CLUSTERING
Estimation of Power Spectra
Velocity Distortions in Power Spectrum
Methods for Estimating Power Spectra
Cluster and Percolation Analysis
Minimal Spanning Trees
Cluster Finding Algorithms
Checking for Periodicity
Some Basic Concepts in Statistics
WEB SITE REFERENCES
"I found this book to be a most invigorating read. I recommend it warmly to both of its target audiences, whether astronomers wishing to get a good overview of statistical techniques, or statisticians wanting an account of how statistics is making a difference in cosmology."
-Wilfrid S. Kendall, University of Warwick in the Journal of the American Statistical Association, vol.98, no. 461
"The definitive book on statistical analysis of clustering…Although the book title suggests that this is a book about cosmology, it is in fact about the statistical assessment of clustering in general, and galaxies in particular. This is a fine book, equaling the high technical and pedagogical standards set in the well-known books by Brian Ripley on the same subject. This book complements and extends Ripley's work and so will be invaluable to all who seek to analyze and understand clustering in point data sets in biology, ecology, geophysics, and other fields. From the point of view of cosmology, it is refreshing to see a mathematical approach that is uniformly rigorous without being pedantic. This makes the book eminently suitable for teaching graduate courses in statistics as well as in cosmology,"
- Bernard Jones, Astrophysicist (UK), on Barnes & Noble .com
"… A reference handbook that collects and explains this extensive and seemingly chaotic corpus of techniques, data, and models and that tries to relate all of these to the extent to which this is possible, was greatly needed. This book in my view manages to do this. In it are collected in a readable and very well-structured manner the diverse statistical techniques used in this type of studies--and applicable to many other studies as well--the multiple connection existing between these techniques, as well as the empirical basis on which these are applied, i.e. the various available catalogues of extragalactic objects and their differential characteristics. The authors of this book have made a discernible effort to treat in great detail the latest theoretical and observational discoveries in this field. All of this makes this title an extremely useful tool for all of us who work in cosmology."
-Bulletin of the Spanish Astronomical Society
"…an important contribution to the field…an excellent source for practitioners of observational cosmology, graduate students, and statisticians, …a valuable and timely book."
-The Observatory, vol. 122, no. 1173,April 2003