Handbook of approximate Bayesian computation

679 Pages·2019·12.25 MB·English

by  Scott A, Beaumont, Mark A., Fan, Yanan, Sisson

Handbook of
Approximate Bayesian
Computation
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Handbook of
Approximate Bayesian
Computation
Edited by
S. A. Sisson
Y. Fan
M. A. Beaumont
CRC Press
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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
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Contents
Preface ix
Editors xi
Contributors xiii
I Methods 1
1 Overview of ABC 3
S. A. Sisson, Y. Fan, and M. A. Beaumont
2 On the History of ABC 55
Simon Tavar´e
3 Regression Approaches for ABC 71
Michael G.B. Blum
4 ABC Samplers 87
S. A. Sisson and Y. Fan
5 Summary Statistics 125
Dennis Prangle
6 Likelihood-Free Model Choice 153
Jean-Michel Marin, Pierre Pudlo, Arnaud Estoup,
and Christian Robert
7 ABC and Indirect Inference 179
Christopher C. Drovandi
8 High-Dimensional ABC 211
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 243
Christophe Andrieu, Anthony Lee, and Matti Vihola
v
vi Contents
10 Asymptotics of ABC 269
Paul Fearnhead
11 Informed Choices: How to Calibrate ABC
with Hypothesis Testing 289
Oliver Ratmann, Anton Camacho, Sen Hu, and Caroline Colijn
12 Approximating the Likelihood in ABC 321
Christopher C. Drovandi, Clara Grazian, Kerrie Mengersen,
and Christian Robert
13 A Guide to General-Purpose ABC Software 369
Athanasios Kousathanas, Pablo Duchen, and Daniel Wegmann
14 Divide and Conquer in ABC: Expectation-Propagation
Algorithms for Likelihood-Free Inference 415
Simon Barthelm´e, Nicolas Chopin, and Vincent Cottet
II Applications 435
15 Sequential Monte Carlo-ABC Methods for Estimation
of Stochastic Simulation Models of the Limit Order
Book 437
Gareth W. Peters, Efstathios Panayi, and Francois Septier
16 Inferences on the Acquisition of Multi-Drug
Resistance in Mycobacterium Tuberculosis Using
Molecular Epidemiological Data 481
Guilherme S. Rodrigues, Andrew R. Francis, S. A. Sisson,
and Mark M. Tanaka
17 ABC in Systems Biology 513
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 541
Arnaud Estoup, Paul Verdu, Jean-Michel Marin,
Christian Robert, Alex Dehne-Garcia, Jean-Marie Cornuet,
and Pierre Pudlo
19 ABC for Climate: Dealing with Expensive Simulators 569
Philip B. Holden, Neil R. Edwards, James Hensman,
and Richard D. Wilkinson
Contents vii
20 ABC in Ecological Modelling 597
Matteo Fasiolo and Simon N. Wood
21 ABC in Nuclear Imaging 623
Y. Fan, Steven R. Meikle, Georgios I. Angelis,
and Arkadiusz Sitek
Index 649
Preface
Approximate Bayesian computation (ABC) is now recognised as the first
member of the class of ‘likelihood-free’ methods, which have been instrumental
in driving research in Monte Carlo methods over the past decade. ABC origi-
nated from the need to address challenging inferential problems in population
genetics, where the complexity of a model meant that the associated likeli-
hood function was computationally intractable and could not be evaluated
numerically in any practical amount of time. At its heart, ABC is a very sim-
ple method: numerical evaluation of the likelihood function is replaced with
an assessment of how likely it is the model could have produced the observed
data, based on simulating pseudo-data from the model and comparing it to
the observed data.
The idea is remarkably simple, but this simplicity also means that ABC
methods are highly accessible as analysis tools in a manner similar to the way
in which the accessibility of the Metropolis–Hastings algorithm was respon-
sible for the propagation of Bayesian inferential methods in the 1990s. The
last ten years have seen a surge in interest from the statistical community,
as researchers have realised how powerful ABC can be as a computational
technique. Major advances have been made in terms of computation and the-
ory. In addition, ABC methods have been extensively applied to wide ranging
and diverse applications in many disciplines. With such rapid developments,
it seemed to us that now was a good time to put together an overview of ABC
research and its applications. This will be the first book that synthesises the
most important aspects of ABC research within a single volume.
This handbook is intended to be a comprehensive reference for both devel-
opers and users of ABC methodology. While ABC methods are still relatively
new, in this Handbook, we have attempted to include a substantial amount
of the fundamental ideas so that the material covered will be relevant for
some time. Graduate students and researchers new to ABC wishing to become
acquainted with the field will be able to find instruction on the basic theory
and algorithms. Many chapters are written in tutorial style with detailed
illustrations and examples. Part I first provides an overview of the basic
ABC method and then some history on it’s developmental origins. This is fol-
lowed by detailed expositions on various aspects of ABC techniques, including
algorithm development, construction and choice of summary statistics, model
choice, asymptotic theory, and variants and extensions of ABC algorithms
that deal with particular modelling situations. A purpose-written chapter on
software available for implementing ABC methods is also provided.
ix