MARKOV POINT PROCESSES AND THEIR APPLICATIONS

Transcription

1 MARKOV POINT PROCESSES AND THEIR APPLICATIONS

2 This page is intentionally left blank

3 MARKOV POINT PROCESSES AND THEIR APPLICATIONS M. N. M. van Lieshout Centrum voor Wiskunde en Informatica The Netherlands Imperial College Press

4 Published by Imperial College Press 57 Shelton Street Covent Garden London WC2H 9HE Distributed by Markov Point Processes and Their Applications Downloaded from World Scientific Publishing Co. Pte. Ltd. P O Box 128, Farrer Road, Singapore USA office: Suite 1B, 1060 Main Street, River Edge, NJ UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing -in-publication Data A catalogue record for this book is available from the British Library. MARKOV POINT PROCESSES AND THEIR APPLICATIONS Copyright 2000 by Imperial College Press All rights reserved. This book, or parts thereof may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN This book is printed on acid -free paper. Printed in Singapore by Uto-Print

5 In memory of Nic. van Lieshout

6 This page is intentionally left blank

7 Contents Markov Point Processes and Their Applications Downloaded from Chapter 1 Point Processes Introduction Definitions and notation Simple point processes Finite point processes Poisson point processes Finite point processes specified by a density Campbell and moment measures Interior and exterior conditioning A review of Palm theory A review of conditional intensities Chapter 2 Markov Point Processes Ripley-Kelly Markov point processes The Hammersley-Clifford theorem Markov marked point processes Nearest-neighbour Markov point processes Connected component Markov point processes Chapter 3 Statistical Inference Introduction The Metropolis-Hastings algorithm Conditional simulation Spatial birth-and-death processes Exact simulation vii

8 viii Contents Markov Point Processes and Their Applications Downloaded from Auxiliary variables and the Gibbs sampler Maximum likelihood estimation Estimation based on the conditional intensity Takacs-Fiksel estimation Maximum pseudo-likelihood estimation Goodness of fit testing Discussion Chapter 4 Applications Modelling spatial patterns Pairwise interaction processes Area-interaction processes Shot noise and quermass-interaction processes Morphologically smoothed area-interaction processes Hierarchical and transformed processes Cluster processes Case study Exploratory analysis Model fitting Interpolation and extrapolation Model Posterior sampling Monotonicity properties and coupling from the past Bibliography 157 Index 173