E-Book, Englisch, 456 Seiten
Martinez / Saar Statistics of the Galaxy Distribution
Erscheinungsjahr 2010
ISBN: 978-1-4200-3616-9
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
E-Book, Englisch, 456 Seiten
ISBN: 978-1-4200-3616-9
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
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.
Zielgruppe
Post-graduate students, academics, and researchers in astrophysics, cosmology, and statistics
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
THE CLUMPY UNIVERSE
Galaxies
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
Introduction
The Friedmann-Robertson-Walker Universe
Basic Observational Data
COSMOLOGICAL POINT PROCESSES
Introduction
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
Introduction
Fractal Models for the Universe
Tests on Projected Data
Fractal Dimensions
Multifractal Measures
Multiscaling
Lacunarity
STATISTICAL AND GEOMETRICAL MODELS
Introduction
The Neyman-Scott Process and Related Models
The Voronoi Model
Statistical Models for the Counts in Cells
FORMATION OF STRUCTURE
Introduction
Dynamics of Structure
The Linear Approximation
Exact Solutions
Numerical Experiments
RANDOM FIELDS IN COSMOLOGY
Introduction
Random Fields
Gaussian Random Fields
Realizations of Random Fields
Non-Gaussian Fields
Statistics of Peaks in Gaussian Random Fields
Press-Schecter Method
Halo Model of Galaxy Clustering
Stochastic and Nonlinear Biasing
FOURIER ANALYSIS OF CLUSTERING
Introduction
Estimation of Power Spectra
Redshift Distortions
Velocity Distortions in Power Spectrum
Methods for Estimating Power Spectra
Bispectrum
Low-Dimensional Samples
COSMOGRAPHY
Introduction
Potent Recipe
Wiener Filtering
Constrained Fields
Time Machines
Gravitational Lensing
STRUCTURE STATISTICS
Introduction
Topological Description
Structure Functions
Cluster and Percolation Analysis
Minimal Spanning Trees
Wavelets
Cluster Finding Algorithms
Void Statistics
Checking for Periodicity
APPENDICES
Coordinate Transformations
Some Basic Concepts in Statistics
REFERENCES
WEB SITE REFERENCES
INDEX
