Monte Carlo and quasi-Monte Carlo methods, MCQMC 2018, Rennes

533 Pages·2020·5.818 MB·English

by  Tuffin B., L'Ecuyer P (ed.)

Springer Proceedings in Mathematics & Statistics
Bruno Tuffin
Pierre L’Ecuyer   Editors
Monte
Carlo and
Quasi-Monte
Carlo Methods
MCQMC 2018, Rennes, France, July 1–6
Springer Proceedings in Mathematics &
Statistics
Volume 324
Springer Proceedings in Mathematics & Statistics
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Bruno Tuf n Pierre L Ecuyer
(cid:129)
Editors
Monte Carlo and
Quasi-Monte Carlo Methods
–
MCQMC 2018, Rennes, France, July 1 6
123
Editors
BrunoTuffin Pierre L’Ecuyer
INRIA RennesBretagne-Atlantique Départementd’informatiqueetdeRecherche
CampusUniverstaire deBeaulieu Opérationnelle (DIRO)
Rennes,France UniversitédeMontréal
Montreal,QC, Canada
ISSN 2194-1009 ISSN 2194-1017 (electronic)
SpringerProceedings in Mathematics& Statistics
ISBN978-3-030-43464-9 ISBN978-3-030-43465-6 (eBook)
https://doi.org/10.1007/978-3-030-43465-6
Mathematics Subject Classification (2010): 65C05, 62D05, 62E10, 65B99, 62-06, 65Cxx, 62Pxx,
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Preface
This volume represents the refereed proceedings of the Thirteenth International
Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific
Computing,whichwasheldattheUniversityofRennes,France,andorganizedby
Inria, from 1–6 July, 2018. It contains a limited selection of articles based on
presentationsmadeattheconference.Theprogramwasarrangedwiththehelpofan
international committee consisting of the following members:
Zdravko I. Botev (Australia, University of New South Wales)
Hector Cancela (Uruguay, Universidad de la Republica)
Frédéric Cérou (France, Inria)
Nicolas Chopin (France, ENSAE)
Ronald Cools (Belgium, KU Leuven)
Josef Dick (Australia, University of New South Wales)
Arnaud Doucet (UK, Oxford University)
Paul Dupuis (USA, Brown University)
Michael B. Giles (UK, Oxford University)
Mark Girolami (UK, Uinversity of Warwick)
Paul Glasserman (USA, Columbia University)
Peter W. Glynn (USA, Stanford University)
Michael Gnewuch (Germany, Universität Kiel)
Emmanuel Gobet (France, Ecole Polytechnique)
Takashi Goda (Japan, The University of Tokyo)
Arnaud Guyader (France, Université Pierre et Marie Curie)
Stefan Heinrich (Germany, Universität Kaiserslautern)
Fred J. Hickernell (USA, Illinois Institute of Technology)
Aicke Hinrichs (Austria, JKU Linz)
Wenzel Jakob (Switzerland, ETH and Disney)
Alexander Keller (Germany, NVIDIA)
Dirk P. Kroese (Australia, University of Queensland)
Frances Y. Kuo (Australia, University of New South Wales)
Gerhard Larcher (Austria, JKU Linz)
v
vi Preface
Christian Lécot (France, Université de Savoie)
Pierre L’Ecuyer (Canada, Université de Montréal)
Christiane Lemieux (Canada, University of Waterloo)
Faming Liang (USA, University of Florida, Gainesville)
Makoto Matsumoto (Japan, Hiroshima University)
Eric Moulines (France, Ecole Polytechnique)
Thomas Mueller-Gronbach (Germany, Universität Passau)
Harald Niederreiter (Austria, Academy of Sciences)
Erich Novak (Germany, Universität Jena)
Dirk Nuyens (Belgium, KU Leuven)
Art B. Owen (USA, Stanford University)
Gareth Peters (UK, University College London)
Friedrich Pillichshammer (Austria, JKU Linz)
Klaus Ritter (Germany, Universität Kaiserslauten)
Gerardo Rubino (France, Inria)
Wolfgang Ch. Schmid (Austria, Universität Salzburg)
Ian H. Sloan (Australia, University of New South Wales)
Raul Tempone (Saudi Arabia, KAUST)
Xiaoqun Wang (China, Tsinghua University)
Grzegorz W. Wasilkowski (USA, University of Kentucky)
Henryk Wozniakowski (USA, Columbia University).
This conference continued the tradition of biennial MCQMC conferences initi-
ated by Harald Niederreiter. They were begun at the University of Nevada in Las
Vegas, Nevada, USA, inJune 1994 and followed by conferences at the University
of Salzburg, Austria, in July 1996; the Claremont Colleges in Claremont,
California, USA, in June 1998; Hong Kong Baptist University in Hong Kong,
China, in November 2000; the National University of Singapore, Republic of
Singapore, in November 2002; the Palais des Congrès in Juan-les-Pins, France, in
June 2004; Ulm University, Germany, in July 2006; Université de Montréal,
Canada, in July 2008; University of Warsaw, Poland, in August 2010; the
UniversityofNewSouthWales,Sydney,Australia,inFebruary2012;KULeuven,
Belgium, in April 2014; and Stanford University, USA, in August 2016. The next
MCQMC conference will be held in Oxford, UK, on August 9–14, 2020.
The proceedings of these previous conferences were all published by
Springer-Verlag, under the following titles:
(cid:129) Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing
(H. Niederreiter and P. J.-S. Shiue, eds.)
(cid:129) Monte Carlo and Quasi-Monte Carlo Methods 1996 (H. Niederreiter,
P. Hellekalek, G. Larcher and P. Zinterhof, eds.)
(cid:129) Monte Carlo and Quasi-Monte Carlo Methods 1998 (H. Niederreiter and
J. Spanier, eds.)
(cid:129) Monte Carlo and Quasi-Monte Carlo Methods 2000 (K.-T. Fang,
F. J. Hickernell and H. Niederreiter, eds.)
Preface vii
(cid:129) Monte Carlo and Quasi-Monte Carlo Methods 2002 (H. Niederreiter, ed.)
(cid:129) Monte Carlo and Quasi-Monte Carlo Methods 2004 (H. Niederreiter and
D. Talay, eds.)
(cid:129) MonteCarloandQuasi-MonteCarloMethods2006(A.KellerandS.Heinrich
and H. Niederreiter, eds.)
(cid:129) MonteCarloandQuasi-MonteCarloMethods2008(P.L’EcuyerandA.Owen,
eds.)
(cid:129) Monte Carlo and Quasi-Monte Carlo Methods 2010 (L. Plaskota and
H. Woźniakowski, eds.)
(cid:129) Monte Carlo and Quasi-Monte Carlo Methods 2012 (J. Dick, F. Y. Kuo,
G. W. Peters and I. Sloan, eds.)
(cid:129) MonteCarloand Quasi-Monte Carlo Methods2014 (R. Cools andD.Nuyens,
eds.)
(cid:129) Monte Carlo and Quasi-Monte Carlo Methods 2016 (A. Owen and
P. W. Glynn, eds.).
The program of the conference was rich and varied with over regular 190 talks
being presented and more than 230 registered participants. Highlights were the
invited plenary talks given by Christophe Andrieu (Bristol, UK), Pierre
Henry-Labordère (Société Générale, Paris, France), Éric Moulines (Ecole
Polytechnique, France), Marvin Nakayama (NJIT, USA), Barry L. Nelson
(Northwestern University, USA), Friedrich Pillichshammer (JKU Linz, Austria),
Clémentine Prieur (Université Grenoble Alpes & Inria, France), and Christoph
Schwab (ETH Zurich, Swizerland).
Thepapersinthisvolumewerecarefullyscreenedandcoverboththetheoryand
the applications of Monte Carlo and quasi-Monte Carlo methods. We thank the
anonymous reviewers for their reports and many others who contributed enor-
mously to the excellent quality of the conference presentations and to the high
standardsforpublicationintheseproceedingsbycarefulreviewoftheabstractsand
manuscripts that were submitted.
We gratefully acknowledge generous financial support of the conference by
Inria, the University of Rennes 1, Région Bretagne, and Rennes Métropole.
Finally, we want to express our gratitude to Springer-Verlag for publishing this
volume.
Rennes, France Pierre L’Ecuyer
Montreal, Canada Bruno Tuffin
September 2019
Contents
Invited Talks
A Tutorial on Quantile Estimation via Monte Carlo . . . . . . . . . . . . . . . 3
Hui Dong and Marvin K. Nakayama
Multilevel Quasi-Monte Carlo Uncertainty Quantification
for Advection-Diffusion-Reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Lukas Herrmann and Christoph Schwab
Selecting the Best Simulated System: Thinking Differently About
an Old Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Barry L. Nelson
Discrepancy of Digital Sequences: New Results on a Classical
QMC Topic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Friedrich Pillichshammer
Regular Talks
Network Structure Change Point Detection by Posterior Predictive
Discrepancy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Lingbin Bian, Tiangang Cui, Georgy Sofronov, and Jonathan Keith
Stochastic Methods for Solving High-Dimensional Partial
Differential Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Marie Billaud-Friess, Arthur Macherey, Anthony Nouy
and Clémentine Prieur
Massively Parallel Construction of Radix Tree Forests
for the Efficient Sampling of Discrete or Piecewise Constant
Probability Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Nikolaus Binder and Alexander Keller
ix
x Contents
An Adaptive Algorithm Employing Continuous
Linear Functionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
Yuhan Ding, Fred J. Hickernell, and Lluís Antoni Jiménez Rugama
Constructing QMC Finite Element Methods for Elliptic PDEs
with Random Coefficients by a Reduced CBC Construction . . . . . . . . . 183
Adrian Ebert, Peter Kritzer, and Dirk Nuyens
Sudoku Latin Square Sampling for Markov Chain Simulation . . . . . . . 207
RamiElHaddad,JosephElMaalouf,ChristianLécot,andPierreL’Ecuyer
Avoiding the Sign Problem in Lattice Field Theory. . . . . . . . . . . . . . . . 231
Tobias Hartung, Karl Jansen, Hernan Leövey, and Julia Volmer
OnHybridPointSetsStemmingfromHalton-TypeHammersleyPoint
Sets and Polynomial Lattice Point Sets . . . . . . . . . . . . . . . . . . . . . . . . . 251
Roswitha Hofer
Robust Estimation of the Mean with Bounded Relative Standard
Deviation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
Mark Huber
Infinite Swapping Algorithm for Training Restricted Boltzmann
Machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
Henrik Hult, Pierre Nyquist, and Carl Ringqvist
Sensitivity Ranks by Monte Carlo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
Ian Iscoe and Alexander Kreinin
Lower Bounds on the L Discrepancy of Digital NUT Sequences. . . . . . 329
p
Ralph Kritzinger and Friedrich Pillichshammer
Randomized QMC Methods for Mixed-Integer Two-Stage Stochastic
Programs with Application to Electricity Optimization . . . . . . . . . . . . . 345
H. Leövey and W. Römisch
Approximating Gaussian Process Emulators with Linear Inequality
Constraints and Noisy Observations via MC and MCMC . . . . . . . . . . . 363
Andrés F. López-Lopera, François Bachoc, Nicolas Durrande,
Jérémy Rohmer, Déborah Idier, and Olivier Roustant
A Multilevel Monte Carlo Asymptotic-Preserving Particle Method
for Kinetic Equations in the Diffusion Limit . . . . . . . . . . . . . . . . . . . . . 383
Emil Løvbak, Giovanni Samaey, and Stefan Vandewalle
Randomized Global Sensitivity Analysis and Model Robustness . . . . . . 403
David Mandel and Giray Ökten
Rapid Covariance-Based Sampling of Linear SPDE Approximations
in the Multilevel Monte Carlo Method. . . . . . . . . . . . . . . . . . . . . . . . . . 423
Andreas Petersson