Random Patterns and Structures in Spatial Data

Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
Preface
1. Introduction: what this book is about
	1.1. Patterns and structures in spatial data
	1.2. Pattern detection problem
	1.3. Pattern characterisation problem
	1.4. Structure of the book
I. Define the pattern: probabilistic modelling
	2. Marked point processes
		2.1. Construction and definition
		2.2. Characterisation of point processes
			2.2.1. Moment measures. Campbell measures. Palm distributions.
			2.2.2. Summary statistics for stationary point processes
		2.3. The Poisson point process
		2.4. Point processes with interactions
			2.4.1. Point processes described by a probability density
			2.4.2. Markov point processes
	3. Applications
		3.1. Galactic filaments: Candy and Bisous models
			3.1.1. Data presentation and problem formulation
			3.1.2. Modelling the data term
			3.1.3. Modelling objects interactions: Candy and Bisous models
		3.2. Clusters in animal epidemiology
			3.2.1. Data presentation and problem formulation
			3.2.2. Modelling the data term
			3.2.3. Modelling objects interaction: mixture of the Strauss and the area-interaction processes
		3.3. Habitat fragmentation
		3.4. Collaborative social networks
		3.5. Landscape modelling using T–tessellations
			3.5.1. Space of T–tessellations
			3.5.2. Completely random T–tessellations
			3.5.3. Gibbs models for T–tessellations
II. Build the pattern: Markov chains Monte Carlo simulation
	4. Markov chains: notions, properties and simulation algorithms
		4.1. “Classical” MCMC simulation
		4.2. Metropolis Hastings algorithm for marked point processes
			4.2.1. Algorithm presentation
			4.2.2. Convergence properties
		4.3. “Perfect” MCMC simulation
			4.3.1. Perfect simulation for marked point processes
			4.3.2. Spatial birth-and-death processes
			4.3.3. CFTP algorithms for marked point processes
	5. Applications
		5.1. Building tailored to the model simulation algorithms
			5.1.1. Simulation study of the tailored dynamics built for sampling the Candy model
			5.1.2. Monte Carlo dynamics for sampling T–tessellations
		5.2. Analysis of some exact simulation algorithms for marked point processes
			5.2.1. Clan of ancestors
			5.2.2. Exact Metropolis-Hastings
			5.2.3. Exact Gibbs sampler
			5.2.4. Simulation study
III. Describe the pattern: statistical inference
	6. Mathematical tools for statistical pattern detection and characterisation
		6.1. Questions related to the pattern
		6.2. Some tools for pattern detection
			6.2.1. Simulated annealing: global maximisation of point process probability densities
			6.2.2. Level sets based estimator for robust pattern detection
		6.3. Pattern characterisation through parameter estimation
			6.3.1. Maximum pseudo-likelihood
			6.3.2. Monte Carlo maximum likelihood
			6.3.3. EM algorithm: parameter estimation for incomplete observed data
		6.4. Pattern characterisation through posterior sampling
			6.4.1. Auxiliary variable MH sampler
			6.4.2. Exchange MH algorithm
			6.4.3. Approximate Bayesian Computation
			6.4.4. Posterior approximation via the ABC Shadow algorithm
			6.4.5. Shadow Simulated Annealing algorithm for parameter estimation
	7. Applications
		7.1. Bayesian detection of patterns in spatial data
			7.1.1. Clusters detection in animal epidemiological data
			7.1.2. Clusters detection in cosmological data
			7.1.3. Bias effects minimisation in cosmological data
			7.1.4. Galactic filaments detection in cosmological data
		7.2. Evaluation and analysis: does the detected pattern really exist?
			7.2.1. Verification of the clusters detection in epidemiological data
			7.2.2. Verification of the galactic filaments detection
		7.3. Level sets for the study of planetary perturbations on comets dynamics
			7.3.1. Order statistics
			7.3.2. Stable distributions models
			7.3.3. A verification of the results through Opik’s theory
		7.4. Morpho-statistical characterisation of patterns
			7.4.1. Segment pattern characterisation via maximum likelihood estimation of the Candy model
			7.4.2. Parametric inference for the Candy model using the ABC Shadow and the SSA algorithms
			7.4.3. Morpho-statistical characterisation of the spatial galaxy distribution through Gibbs point processes
			7.4.4. Morpho-statistical description of collaborative social networks
			7.4.5. Agricultural landscape characterisation through Gibbs T–tesselations
A. Appendices
	A.1. DRlib C++ library
	A.2. MHDeath procedure
Bibliography
Index