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Handbook of Approximate Bayesian Computation

Chapman & Hall/CRC Handbooks of Modern Statistical Methods Series Editor Garrett Fitzmaurice, Department of Biostatistic, Harvard School of Public Health, Boston, MA, U.S.A. The objective of the series is to provide high-quality volumes covering the state-of-the-art in the theory and applications of statistical methodology. The books in the series are thoroughly edited and present comprehensive, coherent, and unified summaries of specific methodological topics from statistics. The chapters are written by the leading researchers in the field, and present a good balance of theory and application through a synthesis of the key methodological developments and examples and case studies using real data. Longitudinal Data Analysis Edited by Garrett Fitzmaurice, Marie Davidian, Geert Verbeke, and Geert Molenberghs Handbook of Spatial Statistics Edited by Alan E. Gelfand, Peter J. Diggle, Montserrat Fuentes, and Peter Guttorp Handbook of Markov Chain Monte Carlo Edited by Steve Brooks, Andrew Gelman, Galin L. Jones, and Xiao-Li Meng Handbook of Survival Analysis Edited by John P. Klein, Hans C. van Houwelingen, Joseph G. Ibrahim, and Thomas H. Scheike Handbook of Mixed Membership Models and Their Applications Edited by Edoardo M. Airoldi, David M. Blei, Elena A. Erosheva, and Stephen E. Fienberg Handbook of Missing Data Methodology Edited by Geert Molenberghs, Garrett Fitzmaurice, Michael G. Kenward, Anastasios Tsiatis, and Geert Verbeke Handbook of Design and Analysis of Experiments Edited by Angela Dean, Max Morris, John Stufken, and Derek Bingham Handbook of Cluster Analysis Edited by Christian Hennig, Marina Meila, Fionn Murtagh, and Roberto Rocci Handbook of Discrete-Valued Time Series Edited by Richard A. Davis, Scott H. Holan, Robert Lund, and Nalini Ravishanker Handbook of Big Data Edited by Peter Bühlmann, Petros Drineas, Michael Kane, and Mark van der Laan Handbook of Spatial Epidemiology Edited by Andrew B. Lawson, Sudipto Banerjee, Robert P. Haining, and María Dolores Ugarte Handbook of Neuroimaging Data Analysis Edited by Hernando Ombao, Martin Lindquist, Wesley Thompson, and John Aston Handbook of Statistical Methods and Analyses in Sports Edited by Jim Albert, Mark E. Glickman, Tim B. Swartz, Ruud H. Koning Handbook of Methods for Designing, Monitoring, and Analyzing Dose-Finding Trials Edited by John O’Quigley, Alexia Iasonos, Björn Bornkamp Handbook of Quantile Regression Edited by Roger Koenker, Victor Chernozhukov, Xuming He, and Limin Peng Handbook of Environmental and Ecological Statistics Edited by Alan E. Gelfand, Montserrat Fuentes, Jennifer A. Hoeting, Richard Lyttleton Smith For more information about this series, please visit: https://www.crcpress.com/go/handbooks

Handbook of Approximate Bayesian Computation Edited by S. A. Sisson Y. Fan M. A. Beaumont

CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2019 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed on acid-free paper International Standard Book Number-13: 978-1-4398-8150-7 (Hardback) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright. com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging‑in‑Publication Data Names: Sisson, S. A. (Scott A), editor. | Fan, Y. (Yanan), editor. | Beaumont, M. A. (Mark A.), editor. Title: Handbook of approximate Bayesian computation / edited by S.A. Sisson, Y. Fan, M.A. Beaumont. Description: Boca Raton, Florida : CRC Press, [2019] | Includes bibliographical references and index. Identifiers: LCCN 2018010970 | ISBN 9781439881507 (hardback : alk. paper) | ISBN 9781315117195 (e-book) | ISBN 9781439881514 (web pdf) | ISBN 9781351643467 (epub) | ISBN 9781351633963 (mobi/kindle) Subjects: LCSH: Bayesian statistical decision theory. | Mathematical analysis. Classification: LCC QA279.5 .H36 2019 | DDC 519.5/42--dc 3 LC record available at https://lccn.loc.gov/2018010970 Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com

Contents Preface Editors Contributors I Methods 1 Overview of ABC S. A. Sisson, Y. Fan, and M. A. Beaumont 2 On the History of ABC Simon Tavar´e 3 Regression Approaches for ABC Michael G.B. Blum 4 ABC Samplers S. A. Sisson and Y. Fan 5 Summary Statistics Dennis Prangle 6 Likelihood-Free Model Choice Jean-Michel Marin, Pierre Pudlo, Arnaud Estoup, and Christian Robert 7 ABC and Indirect Inference Christopher C. Drovandi 8 High-Dimensional ABC David J. Nott, Victor M.-H. Ong, Y. Fan, and S. A. Sisson 9 Theoretical and Methodological Aspects of Markov Chain Monte Carlo Computations with Noisy Likelihoods Christophe Andrieu, Anthony Lee, and Matti Vihola ix xi xiii 1 3 55 71 87 125 153 179 211 243 v

vi 10 Asymptotics of ABC Paul Fearnhead 11 Informed Choices: How to Calibrate ABC with Hypothesis Testing Oliver Ratmann, Anton Camacho, Sen Hu, and Caroline Colijn 12 Approximating the Likelihood in ABC Christopher C. Drovandi, Clara Grazian, Kerrie Mengersen, and Christian Robert 13 A Guide to General-Purpose ABC Software Athanasios Kousathanas, Pablo Duchen, and Daniel Wegmann 14 Divide and Conquer in ABC: Expectation-Propagation Algorithms for Likelihood-Free Inference Simon Barthelm´e, Nicolas Chopin, and Vincent Cottet II Applications 15 Sequential Monte Carlo-ABC Methods for Estimation of Stochastic Simulation Models of the Limit Order Book Gareth W. Peters, Efstathios Panayi, and Francois Septier 16 Inferences on the Acquisition of Multi-Drug Resistance in Mycobacterium Tuberculosis Using Molecular Epidemiological Data Guilherme S. Rodrigues, Andrew R. Francis, S. A. Sisson, and Mark M. Tanaka 17 ABC in Systems Biology Juliane Liepe and Michael P.H. Stumpf 18 Application of ABC to Infer the Genetic History of Pygmy Hunter-Gatherer Populations from Western Central Africa Arnaud Estoup, Paul Verdu, Jean-Michel Marin, Christian Robert, Alex Dehne-Garcia, Jean-Marie Cornuet, and Pierre Pudlo Contents 269 289 321 369 415 435 437 481 513 541 19 ABC for Climate: Dealing with Expensive Simulators 569 Philip B. Holden, Neil R. Edwards, James Hensman, and Richard D. Wilkinson

Contents 20 ABC in Ecological Modelling Matteo Fasiolo and Simon N. Wood 21 ABC in Nuclear Imaging Y. Fan, Steven R. Meikle, Georgios I. Angelis, and Arkadiusz Sitek Index vii 597 623 649

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