## Stochastic Geometry: Likelihood and ComputationStochastic geometry involves the study of random geometric structures, and blends geometric, probabilistic, and statistical methods to provide powerful techniques for modeling and analysis. Recent developments in computational statistical analysis, particularly Markov chain Monte Carlo, have enormously extended the range of feasible applications. Stochastic Geometry: Likelihood and Computation provides a coordinated collection of chapters on important aspects of the rapidly developing field of stochastic geometry, including: o a "crash-course" introduction to key stochastic geometry themes o considerations of geometric sampling bias issues o tesselations o shape o random sets o image analysis o spectacular advances in likelihood-based inference now available to stochastic geometry through the techniques of Markov chain Monte Carlo |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Prof A J Baddeley | 33 |

Sampling and censoring | 37 |

Likelihood inference for spatial point processes | 79 |

Markov chain Monte Carlo and spatial point processes | 141 |

Topics in Voronoi and JohnsonMehl tessellations | 173 |

Mathematical morphology | 199 |

### Common terms and phrases

algorithm applications Baddeley bounded capacity functional censoring chain Monte Carlo clustered computation consider convergence convex corresponding defined definition denote dilation disc distance function distribution erosion example exponential family extract Figure finite geodesic Geyer Gibbs sampler given granulometry function grayscale image grayscale reconstruction image analysis inference Johnson-Mehl tessellations Kaplan-Meier estimator Kendall kernel likelihood line segments linear M0ller Mardia markers Markov chain Markov chain Monte matching mathematical mathematical morphology Matheron maxima maximum MCMC measure method Metropolis-Hastings Metropolis-Hastings algorithm minima Molchanov morphological objects obtained parameter pixel point patterns point processes Poisson process probability problem Procrustes random closed set random compact set random sets region Ripley sampler Section Serra shape space simulation spatial point spectral gap square stationary statistics stochastic geometry Stoyan Strauss process structuring element technique Theorem tion transformations unnormalized density update values Vincent Voronoi Voronoi tessellation watershed