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New statistical tools are changing the ways in which scientists analyze and interpret data and models. Many of these are emerging as a result of the wide availability of inexpensive, high speed computational power. In particular, hierarchical Bayes and Markov Chain Monte Carlo methods for anyalsis provide consistent framework for inference and prediction where information is heterogeneous and uncertain, processes are complex, and responses depend on scale. Nowhere are these methods more promising than in the environmental sciences. Models have developed rapidly, and there is now a requirement for a clear exposition of the methodology through to application for a range of environmental challenges.
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Hierarchical Modelling for the Environmental Sciences This page intentionally left blank Hierarchical Modelling for the Environmental Sciences Statistical Methods and Applications EDITED BY James S. Clark Duke University, USA AND Alan E. Gelfand Duke University, USA 1 3 Great Clarendon Street, Oxford ox2 6dp Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide in Oxford New York Auckland Cape Town Dar es Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shangai Taipei Toronto With offices in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan South Korea Poland Portugal Singapore Switzerland Thailand Turkey Ukraine Vietnam Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries Published in the United States by Oxford University Press Inc., New York © Oxford University Press, 2006 The moral rights of the authors have been asserted Database right Oxford University Press (maker) First published 2006 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this book in any other binding or cover and you must impose the same condition on any acquirer British Library Cataloguing in Publication Data Data available Library of Congress Cataloging in Publication Data Hierarchical modelling for the environmental sciences: statistical methods and applications / edited by James S. Clark and Alan E. Gelfand. p. cm. Includes bibliographical references. ISBN-13: 978–0–19–856966–4 (acid-free paper) ISBN-10: 0–19–856966–1 (acid-free paper) ISBN-13: 978–0–19–856967–1 (pbk. : acid-free paper) ISBN-10: 0–19–856967–X (pbk. : acid-free paper) 1. Bayesian statistical decision theory. 2. Multilevel models (Statistics) 3. Mathematical statistics–Data processing. 4. Environmental sciences–Statistical methods. I. Clark, James Samuel, 1957– II. Gelfand, Alan E., 1945– QA279.5.C647 2006 2005030159 577.01′ 519542—dc22 Typeset by Newgen Imaging Systems (P) Ltd., Chennai, India Printed in Great Britain on acid-free paper by Antony Rowe, Chippenham ISBN 0–19–856966–1 (Hbk) ISBN 0–19–856967–X (Pbk) 10 9 8 7 6 5 4 3 2 1 978–0–19–856966–4 978–0–19–856967–1 Preface New statistical tools are changing the way in which scientists analyze and interpret data and models. Hierarchical Bayes modeling with sampling based methods for fitting and analysis provide a consistent framework for inference and prediction where information is heterogeneous and uncertain, processes are complicated, and responses depend o