Book contents
- Frontmatter
- Contents
- List of contributors
- Preface
- Bibliography of J. F. C. Kingman
- 1 A fragment of autobiography, 1957–1967
- 2 More uses of exchangeability: representations of complex random structures
- 3 Perfect simulation using dominated coupling from the past with application to area-interaction point processes and wavelet thresholding
- 4 Assessing molecular variability in cancer genomes
- 5 Branching out
- 6 Kingman, category and combinatorics
- 7 Long-range dependence in a Cox process directed by an alternating renewal process
- 8 Kernel methods and minimum contrast estimators for empirical deconvolution
- 9 The coalescent and its descendants
- 10 Kingman and mathematical population genetics
- 11 Characterizations of exchangeable partitions and random discrete distributions by deletion properties
- 12 Applying coupon-collecting theory to computer-aided assessments
- 13 Colouring and breaking sticks: random distributions and heterogeneous clustering
- 14 The associated random walk and martingales in random walks with stationary increments
- 15 Diffusion processes and coalescent trees
- 16 Three problems for the clairvoyant demon
- 17 Homogenization for advection-diffusion in a perforated domain
- 18 Heavy traffic on a controlled motorway
- 19 Coupling time distribution asymptotics for some couplings of the Lévy stochastic area
- 20 Queueing with neighbours
- 21 Optimal information feed
- 22 A dynamical-system picture of a simple branching-process phase transition
- Index
3 - Perfect simulation using dominated coupling from the past with application to area-interaction point processes and wavelet thresholding
Published online by Cambridge University Press: 07 September 2011
- Frontmatter
- Contents
- List of contributors
- Preface
- Bibliography of J. F. C. Kingman
- 1 A fragment of autobiography, 1957–1967
- 2 More uses of exchangeability: representations of complex random structures
- 3 Perfect simulation using dominated coupling from the past with application to area-interaction point processes and wavelet thresholding
- 4 Assessing molecular variability in cancer genomes
- 5 Branching out
- 6 Kingman, category and combinatorics
- 7 Long-range dependence in a Cox process directed by an alternating renewal process
- 8 Kernel methods and minimum contrast estimators for empirical deconvolution
- 9 The coalescent and its descendants
- 10 Kingman and mathematical population genetics
- 11 Characterizations of exchangeable partitions and random discrete distributions by deletion properties
- 12 Applying coupon-collecting theory to computer-aided assessments
- 13 Colouring and breaking sticks: random distributions and heterogeneous clustering
- 14 The associated random walk and martingales in random walks with stationary increments
- 15 Diffusion processes and coalescent trees
- 16 Three problems for the clairvoyant demon
- 17 Homogenization for advection-diffusion in a perforated domain
- 18 Heavy traffic on a controlled motorway
- 19 Coupling time distribution asymptotics for some couplings of the Lévy stochastic area
- 20 Queueing with neighbours
- 21 Optimal information feed
- 22 A dynamical-system picture of a simple branching-process phase transition
- Index
Summary
Abstract
We consider perfect simulation algorithms for locally stable point processes based on dominated coupling from the past, and apply these methods in two different contexts. A new version of the algorithm is developed which is feasible for processes which are neither purely attractive nor purely repulsive. Such processes include multiscale area-interaction processes, which are capable of modelling point patterns whose clustering structure varies across scales. The other topic considered is nonparametric regression using wavelets, where we use a suitable area-interaction process on the discrete space of indices of wavelet coefficients to model the notion that if one wavelet coefficient is non-zero then it is more likely that neighbouring coefficients will be also. A method based on perfect simulation within this model shows promising results compared to the standard methods which threshold coefficients independently.
Keywords coupling from the past (CFTP), dominated CFTP, exact simulation, local stability, Markov chain Monte Carlo, perfect simulation, Papangelou conditional intensity, spatial birth-and-death process
AMS subject classification (MSC2010) 62M30, 60G55, 60K35
Introduction
Markov chain Monte Carlo (MCMC) is now one of the standard approaches of computational Bayesian inference. A standard issue when using MCMC is the need to ensure that the Markov chain we are using for simulation has reached equilibrium. For certain classes of problem, this problem was solved by the introduction of coupling from the past (CFTP) (Propp and Wilson, 1996, 1998).
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- Chapter
- Information
- Probability and Mathematical GeneticsPapers in Honour of Sir John Kingman, pp. 64 - 90Publisher: Cambridge University PressPrint publication year: 2010
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