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This text concentrates on what can be achieved using the likelihood/Fisherian methods of taking into account uncertainty when studying a statistical problem. It takes the concept of the likelihood as the best method for unifying the demands of statistical modeling and theory of inference. Every likelihood concept is illustrated with realistic examples ranging from a simple comparison of two accident rates to complex studies that require generalized linear or semiparametric modeling. The emphasis is on likelihood not as just a device used to produce an estimate, but as an important tool for modeling.
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In All Likelihood Statistical Modelling and Inference Using Likelihood Yudi Pawitan UnitJersity College Cork National UnitJersity oj Ireland Cork, Ireland yudiGstat.ucc.ie CLARENDONPRESS·OXFORD - 2001 OXFORD UNIVlIIlSITY puss 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 Shanghai Taipei Toronto With offices in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan South Korea Poland Portugal Singapore Switzerland Thailand Thrkey 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 @ Yudi Pawitan, 2001 The moral rights of the author have been asserted Database right Oxford University Press (maker) First published 2001 Reprinted 2003 (with corrections), 2004,2005,2006,2007 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 th\= 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 this same condition on any acquirer. British Library Cataloguing in Publication Data Data available Library of Congress Cataloging in Publication Data ISBN 978 0 19 850765 9 10 9 8 7 6 Typeset by Yudi Pawitan. Printed in Great Britain on acid-free paper by Biddles Ltd, King's Lynn, Norfolk Preface Likelihood is the central concept in statistical modelling and inference. In All Likelihood covers the essential aspects of likelihood-based modelling as well as likelihood's fundamental role in inference. The title is a gentle reminder of the original meaning of 'likelihood' as a measure of uncertainty, a Fisherian view that tends to be forgotten under the weight of likelihood's more technical role. Fisher coined the term 'likelihood' in 1921 to distinguish the method of maximum likelihood from the Bayesian or inverse probability argument. In the early days its application was fairly limited; few statistical techniques from the 1920s to 1950s could be called 'likelihood-based'. To see why, let us consider what we mean by 'statistical activities': • planning: making decisions about the study design or sampling protocol, what measurements to take, stratification, sample size, etc. • describing: summarizing the bulk of data in few quantities, finding or revealing meaningful patterns or trends, etc. • modelling: developing mathematical models with few parameters to represent the patterns, or to explain the variability in terms of relationship between variables. • inferenc