Approximate Bayesian computation with the Wasserstein distance

A growing number of generative statistical models do not permit the numerical evaluation of their likelihood functions. Approximate Bayesian computation has become a popular approach to overcome this issue, in which one simulates synthetic data sets given parameters and compares summaries of these d...

Full description

Saved in:

Bibliographic Details
Published in:	Journal of the Royal Statistical Society. Series B, Statistical methodology Vol. 81; no. 2; pp. 235 - 269
Main Authors:	Bernton, Espen, Jacob, Pierre E., Gerber, Mathieu, Robert, Christian P.
Format:	Journal Article
Language:	English
Published:	Oxford Wiley 01.04.2019 Oxford University Press
Subjects:	Approximate Bayesian computation Bayesian analysis Bayesian theory Biology Computation Computer simulation Data data collection Datasets equations Generative models Hilbert curve Hilbert space Likelihood‐free inference Optimal transport Property Queueing Queues Regression analysis Statistical methods Statistical models Statistics Summaries Time series time series analysis Volatility Wasserstein distance
ISSN:	1369-7412, 1467-9868
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Abstract	A growing number of generative statistical models do not permit the numerical evaluation of their likelihood functions. Approximate Bayesian computation has become a popular approach to overcome this issue, in which one simulates synthetic data sets given parameters and compares summaries of these data sets with the corresponding observed values. We propose to avoid the use of summaries and the ensuing loss of information by instead using the Wasserstein distance between the empirical distributions of the observed and synthetic data. This generalizes the well-known approach of using order statistics within approximate Bayesian computation to arbitrary dimensions. We describe how recently developed approximations of the Wasserstein distance allow the method to scale to realistic data sizes, and we propose a new distance based on the Hilbert space filling curve. We provide a theoretical study of the method proposed, describing consistency as the threshold goes to 0 while the observations are kept fixed, and concentration properties as the number of observations grows. Various extensions to time series data are discussed. The approach is illustrated on various examples, including univariate and multivariate g-and-k distributions, a toggle switch model from systems biology, a queuing model and a Lévy-driven stochastic volatility model.
AbstractList	Summary A growing number of generative statistical models do not permit the numerical evaluation of their likelihood functions. Approximate Bayesian computation has become a popular approach to overcome this issue, in which one simulates synthetic data sets given parameters and compares summaries of these data sets with the corresponding observed values. We propose to avoid the use of summaries and the ensuing loss of information by instead using the Wasserstein distance between the empirical distributions of the observed and synthetic data. This generalizes the well‐known approach of using order statistics within approximate Bayesian computation to arbitrary dimensions. We describe how recently developed approximations of the Wasserstein distance allow the method to scale to realistic data sizes, and we propose a new distance based on the Hilbert space filling curve. We provide a theoretical study of the method proposed, describing consistency as the threshold goes to 0 while the observations are kept fixed, and concentration properties as the number of observations grows. Various extensions to time series data are discussed. The approach is illustrated on various examples, including univariate and multivariate g‐and‐k distributions, a toggle switch model from systems biology, a queuing model and a Lévy‐driven stochastic volatility model. A growing number of generative statistical models do not permit the numerical evaluation of their likelihood functions. Approximate Bayesian computation has become a popular approach to overcome this issue, in which one simulates synthetic data sets given parameters and compares summaries of these data sets with the corresponding observed values. We propose to avoid the use of summaries and the ensuing loss of information by instead using the Wasserstein distance between the empirical distributions of the observed and synthetic data. This generalizes the well‐known approach of using order statistics within approximate Bayesian computation to arbitrary dimensions. We describe how recently developed approximations of the Wasserstein distance allow the method to scale to realistic data sizes, and we propose a new distance based on the Hilbert space filling curve. We provide a theoretical study of the method proposed, describing consistency as the threshold goes to 0 while the observations are kept fixed, and concentration properties as the number of observations grows. Various extensions to time series data are discussed. The approach is illustrated on various examples, including univariate and multivariate g‐and‐k distributions, a toggle switch model from systems biology, a queuing model and a Lévy‐driven stochastic volatility model.
Author	Robert, Christian P. Gerber, Mathieu Jacob, Pierre E. Bernton, Espen
Author_xml	– sequence: 1 givenname: Espen surname: Bernton fullname: Bernton, Espen – sequence: 2 givenname: Pierre E. surname: Jacob fullname: Jacob, Pierre E. – sequence: 3 givenname: Mathieu surname: Gerber fullname: Gerber, Mathieu – sequence: 4 givenname: Christian P. surname: Robert fullname: Robert, Christian P.
BookMark	eNp9kE1LAzEQQIMo-HnxLix4EWFrMkmT5iJY8QsEwSoeQ5qdxZTtbk1StP_e6KoHEeeSHN4bhrdN1tuuRUL2GR2wPCchxumAAWewRraYkKrUIzlaz38udakEg02yHeOM5pGKb5HTs8UidG9-bhMWY7vC6G1buG6-WCabfNcWrz49F-kZiycbI4aY0LdF5WOyrcNdslHbJuLe17tDHi8vHs6vy9u7q5vzs9vSCeBQalFXdMpqKTQKiQJAVwytrqsKUUHFqBtCBWgFp8qB1bKSoNiUI7rhUNd8hxz1e_OxL0uMycx9dNg0tsVuGQ0AV0NKtYSMHv5CZ90ytPk6A0xzJkagWaaOe8qFLsaAtVmEHCGsDKPmI6X5SGk-U2aY_oKd7-ukYH3zt8J65dU3uPpnubmfTMbfzkHvzGLqwo8DUikOjPJ35lCSHQ
CitedBy_id	crossref_primary_10_1016_j_csda_2024_108095 crossref_primary_10_1016_j_ymssp_2021_107954 crossref_primary_10_1093_imaiai_iaae006 crossref_primary_10_1214_25_BA1535 crossref_primary_10_1016_j_eswa_2022_119114 crossref_primary_10_3390_stats4030045 crossref_primary_10_3390_e27070683 crossref_primary_10_1038_s41598_021_96214_w crossref_primary_10_1371_journal_pcbi_1009910 crossref_primary_10_1007_s11222_019_09909_6 crossref_primary_10_1007_s13253_024_00663_5 crossref_primary_10_3847_1538_4365_ad8ebd crossref_primary_10_1016_j_csda_2023_107795 crossref_primary_10_1016_j_microrel_2024_115399 crossref_primary_10_1016_j_jmva_2019_06_008 crossref_primary_10_3390_e22111272 crossref_primary_10_1093_jrsssb_qkae005 crossref_primary_10_1080_03461238_2022_2145577 crossref_primary_10_1007_s13571_019_00208_8 crossref_primary_10_1080_01621459_2022_2060836 crossref_primary_10_1214_22_STS875 crossref_primary_10_1007_s00180_021_01093_4 crossref_primary_10_1111_rssc_12487 crossref_primary_10_1214_24_BA1416 crossref_primary_10_1098_rsos_230275 crossref_primary_10_1016_j_epidem_2025_100855 crossref_primary_10_1109_TNNLS_2025_3551275 crossref_primary_10_1051_epjn_2021001 crossref_primary_10_1093_biomtc_ujaf069 crossref_primary_10_1007_s11222_022_10155_6 crossref_primary_10_1016_j_csda_2023_107764 crossref_primary_10_1016_j_ijepes_2023_109427 crossref_primary_10_1093_biomet_asz008 crossref_primary_10_1007_s11222_022_10092_4 crossref_primary_10_1016_j_jedc_2024_104827 crossref_primary_10_1002_sam_11711 crossref_primary_10_1002_zamm_202200481 crossref_primary_10_1109_ACCESS_2020_3009878 crossref_primary_10_1098_rsos_231697 crossref_primary_10_1080_10618600_2024_2374580 crossref_primary_10_1007_s11222_022_10163_6 crossref_primary_10_1109_TPAMI_2024_3363780 crossref_primary_10_1007_s11222_022_10146_7 crossref_primary_10_1007_s42952_024_00295_y crossref_primary_10_1007_s00180_025_01606_5 crossref_primary_10_1016_j_envsoft_2023_105905 crossref_primary_10_1016_j_watres_2021_117466 crossref_primary_10_3390_biophysica4040039 crossref_primary_10_1016_j_cam_2022_114494 crossref_primary_10_1016_j_engappai_2021_104457 crossref_primary_10_1016_j_ocemod_2023_102275 crossref_primary_10_1371_journal_pone_0236954 crossref_primary_10_1080_00031305_2025_2551223 crossref_primary_10_1371_journal_pone_0285836 crossref_primary_10_1080_10485252_2023_2292690 crossref_primary_10_1111_sjos_12509 crossref_primary_10_1007_s00285_024_02144_2 crossref_primary_10_1080_15376494_2022_2162643 crossref_primary_10_1016_j_insmatheco_2021_06_002 crossref_primary_10_1016_j_ymssp_2022_110012 crossref_primary_10_1111_rssb_12356 crossref_primary_10_1007_s11538_024_01331_y crossref_primary_10_1093_jrsssb_qkad008
Cites_doi	10.1201/9781315117195-4 10.1111/j.1467-8659.2011.02032.x 10.1007/s11222-011-9288-2 10.1016/j.spl.2006.02.001 10.1201/b10956 10.1093/genetics/162.4.2025 10.1023/A:1013120305780 10.1111/rssb.12104 10.1515/sagmb-2012-0069 10.32614/RJ-2015-030 10.1007/978-3-319-33507-0_28 10.1137/130915376 10.1371/journal.pone.0110214 10.1111/rssb.12236 10.1111/j.1467-9868.2012.01046.x 10.1093/biomet/asy027 10.1073/pnas.1208827110 10.1007/978-1-4612-0871-6 10.1007/978-3-319-20828-2 10.1214/13-EJS819 10.1007/s11222-011-9271-y 10.1007/s00332-003-0534-4 10.1214/aop/1176988735 10.1214/18-AOS1746 10.1093/biomet/asu027 10.3982/ECTA9097 10.1534/genetics.108.098129 10.1111/j.1467-9868.2011.01010.x 10.2202/1544-6115.1684 10.1016/j.csda.2011.03.019 10.1090/gsm/058 10.1111/j.1467-9868.2009.00736.x 10.1007/s10851-017-0726-4 10.1093/biomet/asx078 10.1007/s10851-014-0506-3 10.1016/j.jmaa.2017.02.003 10.3390/e19020047 10.1007/s00440-014-0583-7 10.1111/1467-9868.00336 10.1016/j.comgeo.2007.08.003 10.1137/1.9780898717754
ContentType	Journal Article
Copyright	2019 Royal Statistical Society Copyright © 2019 The Royal Statistical Society and Blackwell Publishing Ltd
Copyright_xml	– notice: 2019 Royal Statistical Society – notice: Copyright © 2019 The Royal Statistical Society and Blackwell Publishing Ltd
DBID	AAYXX CITATION 7SC 8BJ 8FD FQK JBE JQ2 L7M L~C L~D 7S9 L.6
DOI	10.1111/rssb.12312
DatabaseName	CrossRef Computer and Information Systems Abstracts International Bibliography of the Social Sciences (IBSS) Technology Research Database International Bibliography of the Social Sciences International Bibliography of the Social Sciences ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional AGRICOLA AGRICOLA - Academic
DatabaseTitle	CrossRef International Bibliography of the Social Sciences (IBSS) Technology Research Database Computer and Information Systems Abstracts – Academic ProQuest Computer Science Collection Computer and Information Systems Abstracts Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional AGRICOLA AGRICOLA - Academic
DatabaseTitleList	AGRICOLA International Bibliography of the Social Sciences (IBSS) CrossRef
DeliveryMethod	fulltext_linktorsrc
Discipline	Statistics Biology
EISSN	1467-9868
EndPage	269
ExternalDocumentID	10_1111_rssb_12312 RSSB12312 26773210
Genre	article
GrantInformation_xml	– fundername: National Science Foundation funderid: DMS‐1712872
GroupedDBID	-~X .3N .4S .DC .GA 05W 10A 1OC 29L 2AX 33P 3SF 4.4 50Y 50Z 51W 51X 52M 52N 52O 52P 52S 52T 52U 52W 52X 5GY 5HH 5LA 5VS 66C 702 7PT 8-0 8-1 8-3 8UM 8VB 930 A03 AAESR AAEVG AAHBH AAONW AAPXW AASGY AAUAY AAXRX AAZKR ABBHK ABCQN ABCUV ABDFA ABEHJ ABEML ABFAN ABIVO ABLJU ABPFR ABPQP ABPTD ABPVW ABWST ABXSQ ABYWD ABZEH ACAHQ ACCZN ACGFS ACIWK ACMTB ACNCT ACPOU ACSCC ACTMH ACUBG ACXBN ACXQS ADBBV ADEOM ADIYS ADIZJ ADKYN ADMGS ADODI ADOZA ADRDM ADVEK ADZMN AEGXH AEIMD AEMOZ AEUPB AFBPY AFEBI AFGKR AFVYC AFXHP AFZJQ AHQJS AIURR AJAOE AJNCP AJXKR AKVCP ALAGY ALMA_UNASSIGNED_HOLDINGS ALRMG ALUQN AMBMR AMVHM AMYDB ARCSS ASPBG ATUGU AUFTA AVWKF AZBYB AZVAB BAFTC BCRHZ BDRZF BHBCM BMNLL BMXJE BNHUX BROTX BRXPI BY8 CAG CJ0 CO8 CS3 D-E DCZOG DPXWK DQDLB DR2 DRFUL DRSTM DSRWC EBA EBO EBR EBS EBU ECEWR EDO EJD EMK F00 F5P G-S G.N GODZA H.T H.X HQ6 HZI HZ~ IHE IPSME IX1 J0M JAAYA JAS JBMMH JBZCM JENOY JHFFW JKQEH JLEZI JLXEF JMS JPL JST K1G K48 LATKE LC2 LC3 LEEKS LH4 LITHE LOXES LP6 LP7 LUTES LW6 LYRES MK4 MRFUL MRSTM MSFUL MSSTM MXFUL MXSTM N04 N05 NF~ NU- O66 O9- OIG P2W P2X P4D PQQKQ Q.N Q11 QB0 QWB R.K RNS ROL ROX RX1 SA0 SUPJJ TH9 TN5 TUS UB1 UPT W8V W99 WBKPD WH7 WIH WIK WOHZO WQJ WYISQ XBAML XG1 YQT ZL0 ZZTAW ~02 ~IA ~KM ~WT .Y3 3-9 31~ AANHP AARHZ AAWIL ABAWQ ABPQH ACBWZ ACFRR ACHJO ACRPL ACYXJ ADNMO ADQBN ADULT AGLNM AGQPQ AIHAF ANFBD AS~ ATGXG AZFZN COF FEDTE FVMVE H13 HF~ HGD HVGLF H~9 NHB RJQFR ZGI AAYXX ABEJV CITATION O8X OJZSN 7SC 8BJ 8FD FQK JBE JQ2 L7M L~C L~D 7S9 L.6
ID	FETCH-LOGICAL-c4232-94fd0b1f649e46e4229d1ea9fddee72d10c52d2ea4307c2a96d6271b3eec559f3
IEDL.DBID	DRFUL
ISICitedReferencesCount	89
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000461872300002&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	1369-7412
IngestDate	Fri Oct 03 00:01:47 EDT 2025 Sun Nov 09 06:52:14 EST 2025 Tue Nov 18 20:52:04 EST 2025 Sat Nov 29 05:52:11 EST 2025 Sun Sep 21 06:18:11 EDT 2025 Thu Jul 03 21:54:10 EDT 2025
IsPeerReviewed	true
IsScholarly	true
Issue	2
Language	English
License	https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c4232-94fd0b1f649e46e4229d1ea9fddee72d10c52d2ea4307c2a96d6271b3eec559f3
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23
PQID	2193148291
PQPubID	39359
PageCount	35
ParticipantIDs	proquest_miscellaneous_2237500962 proquest_journals_2193148291 crossref_primary_10_1111_rssb_12312 crossref_citationtrail_10_1111_rssb_12312 wiley_primary_10_1111_rssb_12312_RSSB12312 jstor_primary_26773210
PublicationCentury	2000
PublicationDate	April 2019
PublicationDateYYYYMMDD	2019-04-01
PublicationDate_xml	– month: 04 year: 2019 text: April 2019
PublicationDecade	2010
PublicationPlace	Oxford
PublicationPlace_xml	– name: Oxford
PublicationTitle	Journal of the Royal Statistical Society. Series B, Statistical methodology
PublicationYear	2019
Publisher	Wiley Oxford University Press
Publisher_xml	– name: Wiley – name: Oxford University Press
References	2015; 162 2013; 1 2012 2011 2018; 105 2006; 76 2015; 51 2009; 181 2002; 12 2015; 77 2015; 10 2009 2003; 13 2011; 30 2018; 80 1994; 22 2008 2011; 55 2011; 10 1994 2004 2003 2017; 451 2013; 7 2015; 7 2012; 74 1997; 102 2017; 59 2002; 64 2002; 162 2013; 12 2013; 75 2019 2018 2017 2013; 81 2016 2017; 19 2015 2008; 41 2013; 110 2014 2013 2014; 9 2011; 240 2012; 22 2010; 72 2014; 101 CGAL Project (2023022101111891300_) 2016 Sagan (2023022101111891300_) 1994 Beaumont (2023022101111891300_) 2002; 162 Fearnhead (2023022101111891300_) 2012; 74 Villani (2023022101111891300_) 2003 Bassetti (2023022101111891300_) 2006; 76 Jiang (2023022101111891300_) 2018 Panaretos (2023022101111891300_) 2018 Villani (2023022101111891300_) 2008 Marin (2023022101111891300_) 2012; 22 Bonassi (2023022101111891300_) 2011; 10 Park (2023022101111891300_) 2016 Mengersen (2023022101111891300_) 2013; 110 Muskulus (2023022101111891300_) 2011; 240 Weed (2023022101111891300_) 2017 Talagrand (2023022101111891300_) 1994; 22 Rubio (2023022101111891300_) 2013; 7 Puccetti (2023022101111891300_) 2017; 451 Rayner (2023022101111891300_) 2002; 12 Kantz (2023022101111891300_) 2004 Thorpe (2023022101111891300_) 2017; 59 Gottschlich (2023022101111891300_) 2014; 9 Del Moral (2023022101111891300_) 2012; 22 Sisson (2023022101111891300_) 2018 Bonneel (2023022101111891300_) 2015; 51 Bernton (2023022101111891300_) 2017 Nunes (2023022101111891300_) 2015; 7 Rabin (2023022101111891300_) 2011 Berndt (2023022101111891300_) 1994 Ramdas (2023022101111891300_) 2017; 19 Miller (2023022101111891300_) 2018 Gerber (2023022101111891300_) 2019 Li (2023022101111891300_) 2018; 105 Mérigot (2023022101111891300_) 2011; 30 Schuhmacher (2023022101111891300_) 2017 Lee (2023022101111891300_) 2012 Filippi (2023022101111891300_) 2013; 12 Lee (2023022101111891300_) 2014; 101 Moeckel (2023022101111891300_) 1997; 102 Peyré (2023022101111891300_) 2018 Frazier (2023022101111891300_) 2018; 105 Schretter (2023022101111891300_) 2016 Sommerfeld (2023022101111891300_) 2018; 80 Fournier (2023022101111891300_) 2015; 162 Cuturi (2023022101111891300_) 2013 Barndorff-Nielsen (2023022101111891300_) 2002; 64 Buchin (2023022101111891300_) 2008; 41 Chopin (2023022101111891300_) 2013; 75 Müller (2023022101111891300_) 2013; 81 Majumdar (2023022101111891300_) 2015 Gerber (2023022101111891300_) 2015; 77 Bonassi (2023022101111891300_) 2015; 10 Basu (2023022101111891300_) 2011 Sousa (2023022101111891300_) 2009; 181 Genevay (2023022101111891300_) 2017 Shestopaloff (2023022101111891300_) 2014 Santambrogio (2023022101111891300_) 2015 Andrieu (2023022101111891300_) 2010; 72 Stark (2023022101111891300_) 2003; 13 Prangle (2023022101111891300_) 2016 Srivastava (2023022101111891300_) 2015 Graham (2023022101111891300_) 2017 del Barrio (2023022101111891300_) 2017 Murray (2023022101111891300_) 2013; 1 Burkard (2023022101111891300_) 2009 Drovandi (2023022101111891300_) 2011; 55
References_xml	– year: 2011 – volume: 51 start-page: 22 year: 2015 end-page: 45 article-title: Sliced and Radon Wasserstein barycenters of measures publication-title: J. Math. Imgng Visn – volume: 75 start-page: 397 year: 2013 end-page: 426 article-title: SMC : an efficient algorithm for sequential analysis of state space models publication-title: J. R. Statist. Soc. – volume: 41 start-page: 2 year: 2008 end-page: 20 article-title: Computing the Fréchet distance between simple polygons publication-title: Computnl Geom. – year: 2009 – volume: 77 start-page: 509 year: 2015 end-page: 579 article-title: Sequential quasi‐Monte Carlo (with discussion) publication-title: J. R. Statist. Soc. – start-page: 199 year: 2015 end-page: 208 – volume: 101 start-page: 655 year: 2014 end-page: 671 article-title: Variance bounding and geometric ergodicity of Markov chain Monte Carlo kernels for approximate Bayesian computation publication-title: Biometrika – year: 2018 article-title: Robust Bayesian inference via coarsening publication-title: J. Am. Statist. Ass. – year: 2019 article-title: Negative association, ordering and convergence of resampling methods publication-title: Ann. Statist – volume: 64 start-page: 253 year: 2002 end-page: 280 article-title: Econometric analysis of realized volatility and its use in estimating stochastic volatility models publication-title: J. R. Statist. Soc. – volume: 105 start-page: 593 year: 2018 end-page: 607 article-title: Asymptotic properties of approximate Bayesian computation publication-title: Biometrika – volume: 162 start-page: 707 year: 2015 end-page: 738 article-title: On the rate of convergence in Wasserstein distance of the empirical measure publication-title: Probab. Theory Reltd Flds – year: 1994 – year: 2014 – volume: 22 start-page: 919 year: 1994 end-page: 959 article-title: The transportation cost from the uniform measure to the empirical measure in dimension 3 publication-title: Ann. Probab. – volume: 105 start-page: 285 year: 2018 end-page: 299 article-title: On the asymptotic efficiency of approximate Bayesian computation estimators publication-title: Biometrika – volume: 55 start-page: 2541 year: 2011 end-page: 2556 article-title: Likelihood‐free Bayesian estimation of multivariate quantile distributions publication-title: Computnl Statist. Data Anal. – volume: 19 year: 2017 article-title: On Wasserstein two‐sample testing and related families of nonparametric tests publication-title: Entropy – volume: 451 start-page: 132 year: 2017 end-page: 145 article-title: An algorithm to approximate the optimal expected inner product of two vectors with given marginals publication-title: J. Math. Anal. Appl. – start-page: 2292 year: 2013 end-page: 2300 – volume: 181 start-page: 1507 year: 2009 end-page: 1519 article-title: Approximate Bayesian computation without summary statistics: the case of admixture publication-title: Genetics – start-page: 1608 year: 2017 end-page: 1617 – year: 2008 – year: 2004 – volume: 80 start-page: 219 year: 2018 end-page: 238 article-title: Inference for empirical Wasserstein distances on finite spaces publication-title: J. R. Statist. Soc. – volume: 76 start-page: 1298 year: 2006 end-page: 1302 article-title: On minimum Kantorovich distance estimators publication-title: Statist. Probab. Lett. – volume: 30 start-page: 1583 year: 2011 end-page: 1592 article-title: A multiscale approach to optimal transport publication-title: Comput. Graph. Forum – start-page: 912 year: 2015 end-page: 920 – start-page: 435 year: 2011 end-page: 446 – start-page: 359 year: 1994 end-page: 370 – volume: 110 start-page: 1321 year: 2013 end-page: 1326 article-title: Bayesian computation via empirical likelihood publication-title: Proc. Natn. Acad. Sci. USA – volume: 10 year: 2011 article-title: Bayesian learning from marginal data in bionetwork models publication-title: Statist. Appl. Genet. Molec. Biol. – year: 2015 – start-page: 87 year: 2018 end-page: 123 – volume: 240 start-page: 45 year: 2011 end-page: 58 article-title: Wasserstein distances in the analysis of time series and dynamical systems publication-title: Physica – volume: 9 start-page: e110214 year: 2014 article-title: The shortlist method for fast computation of the earth mover's distance and finding optimal solutions to transportation problems publication-title: PLOS One – volume: 74 start-page: 419 year: 2012 end-page: 474 article-title: Constructing summary statistics for approximate Bayesian computation: semi‐automatic approximate Bayesian computation (with discussion) publication-title: J. R. Statist. Soc. – start-page: 499 year: 2017 end-page: 508 – volume: 59 start-page: 187 year: 2017 end-page: 210 article-title: A transportation distance for signal analysis publication-title: J. Math. Imgng Visn – volume: 22 start-page: 1167 year: 2012 end-page: 1180 article-title: Approximate Bayesian computational methods publication-title: Statist. Comput. – volume: 12 start-page: 87 year: 2013 end-page: 107 article-title: On optimality of kernels for approximate Bayesian computation using sequential Monte Carlo publication-title: Statist. Appl. Genet. Molec. Biol. – year: 2003 – volume: 72 start-page: 269 year: 2010 end-page: 342 article-title: Particle Markov chain Monte Carlo methods (with discussion) publication-title: J. R. Statist. Soc. – start-page: 531 year: 2016 end-page: 544 – volume: 102 start-page: 187 year: 1997 end-page: 194 article-title: Measuring the distance between time series publication-title: Physica – year: 2016 – volume: 1 start-page: 494 year: 2013 end-page: 521 article-title: On disturbance state‐space models and the particle marginal Metropolis‐Hastings sampler publication-title: J. Uncertnty Quantificn – start-page: 398 year: 2016 end-page: 407 – volume: 13 start-page: 519 year: 2003 end-page: 577 article-title: Delay embeddings for forced system: II, Stochastic forcing publication-title: J. Nonlin. Sci. – volume: 7 start-page: 189 year: 2015 end-page: 205 article-title: abctools: an R package for tuning approximate Bayesian computation analyses publication-title: R J. – volume: 162 start-page: 2025 year: 2002 end-page: 2035 article-title: Approximate Bayesian computation in population genetics publication-title: Genetics – volume: 12 start-page: 57 year: 2002 end-page: 75 article-title: Numerical maximum likelihood estimation for the g‐and‐k and generalized g‐and‐h distributions publication-title: Statist. Comput. – volume: 81 start-page: 1805 year: 2013 end-page: 1849 article-title: Risk of Bayesian inference in misspecified models, and the sandwich covariance matrix publication-title: Econometrica – start-page: 304 year: 2012 end-page: 315 – year: 2018 article-title: Statistical aspects of Wasserstein distances publication-title: A. Rev. Statist. Appl. – volume: 7 start-page: 1632 year: 2013 end-page: 1654 article-title: A simple approach to maximum intractable likelihood estimation publication-title: Electron. J. Statist. – year: 2018 article-title: Computational optimal transport publication-title: Foundns Trends Mach. Learn. – year: 2017 – volume: 10 start-page: 171 year: 2015 end-page: 187 article-title: Sequential Monte Carlo with adaptive weights for approximate Bayesian computation publication-title: Baysn Anal. – start-page: 1711 year: 2018 end-page: 1721 – volume: 22 start-page: 1009 year: 2012 end-page: 1020 article-title: An adaptive sequential Monte Carlo method for approximate Bayesian computation publication-title: Statist. Comput. – start-page: 87 volume-title: Handbook of Approximate Bayesian Computation year: 2018 ident: 2023022101111891300_ doi: 10.1201/9781315117195-4 – start-page: 1711 volume-title: Proc. 21st Int. Conf. Artificial Intelligence and Statistics year: 2018 ident: 2023022101111891300_ – volume-title: Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance year: 2017 ident: 2023022101111891300_ – volume: 30 start-page: 1583 year: 2011 ident: 2023022101111891300_ article-title: A multiscale approach to optimal transport publication-title: Comput. Graph. Forum doi: 10.1111/j.1467-8659.2011.02032.x – volume: 22 start-page: 1167 year: 2012 ident: 2023022101111891300_ article-title: Approximate Bayesian computational methods publication-title: Statist. Comput. doi: 10.1007/s11222-011-9288-2 – start-page: 499 volume-title: Artificial Intelligence and Statistics year: 2017 ident: 2023022101111891300_ – volume-title: Optimal Transport, Old and New year: 2008 ident: 2023022101111891300_ – volume: 76 start-page: 1298 year: 2006 ident: 2023022101111891300_ article-title: On minimum Kantorovich distance estimators publication-title: Statist. Probab. Lett. doi: 10.1016/j.spl.2006.02.001 – volume-title: Statistical Inference: the Minimum Distance Approach year: 2011 ident: 2023022101111891300_ doi: 10.1201/b10956 – volume-title: ) Central limit theorems for empirical transportation year: 2017 ident: 2023022101111891300_ – volume: 162 start-page: 2025 year: 2002 ident: 2023022101111891300_ article-title: Approximate Bayesian computation in population genetics publication-title: Genetics doi: 10.1093/genetics/162.4.2025 – volume: 12 start-page: 57 year: 2002 ident: 2023022101111891300_ article-title: Numerical maximum likelihood estimation for the g-and-k and generalized g-and-h distributions publication-title: Statist. Comput. doi: 10.1023/A:1013120305780 – volume: 77 start-page: 509 year: 2015 ident: 2023022101111891300_ article-title: Sequential quasi-Monte Carlo (with discussion) publication-title: J. R. Statist. Soc. doi: 10.1111/rssb.12104 – volume: 10 start-page: 171 year: 2015 ident: 2023022101111891300_ article-title: Sequential Monte Carlo with adaptive weights for approximate Bayesian computation publication-title: Baysn Anal. – volume: 12 start-page: 87 year: 2013 ident: 2023022101111891300_ article-title: On optimality of kernels for approximate Bayesian computation using sequential Monte Carlo publication-title: Statist. Appl. Genet. Molec. Biol. doi: 10.1515/sagmb-2012-0069 – volume: 7 start-page: 189 year: 2015 ident: 2023022101111891300_ article-title: abctools: an R package for tuning approximate Bayesian computation analyses publication-title: R J. doi: 10.32614/RJ-2015-030 – start-page: 531 volume-title: Monte Carlo and Quasi-Monte Carlo Methods year: 2016 ident: 2023022101111891300_ doi: 10.1007/978-3-319-33507-0_28 – volume: 1 start-page: 494 year: 2013 ident: 2023022101111891300_ article-title: On disturbance state-space models and the particle marginal Metropolis-Hastings sampler publication-title: J. Uncertnty Quantificn doi: 10.1137/130915376 – volume: 9 start-page: e110214 year: 2014 ident: 2023022101111891300_ article-title: The shortlist method for fast computation of the earth mover’s distance and finding optimal solutions to transportation problems publication-title: PLOS One doi: 10.1371/journal.pone.0110214 – volume: 240 start-page: 45 year: 2011 ident: 2023022101111891300_ article-title: Wasserstein distances in the analysis of time series and dynamical systems publication-title: Physica – start-page: 912 volume-title: Artificial Intelligence and Statistics year: 2015 ident: 2023022101111891300_ – volume: 80 start-page: 219 year: 2018 ident: 2023022101111891300_ article-title: Inference for empirical Wasserstein distances on finite spaces publication-title: J. R. Statist. Soc. doi: 10.1111/rssb.12236 – volume: 75 start-page: 397 year: 2013 ident: 2023022101111891300_ article-title: SMC2: an efficient algorithm for sequential analysis of state space models publication-title: J. R. Statist. Soc. doi: 10.1111/j.1467-9868.2012.01046.x – start-page: 359 volume-title: Using dynamic time warping to find patterns in time series year: 1994 ident: 2023022101111891300_ – start-page: 2292 volume-title: Sinkhorn distances: lightspeed computation of optimal transport year: 2013 ident: 2023022101111891300_ – volume: 105 start-page: 593 year: 2018 ident: 2023022101111891300_ article-title: Asymptotic properties of approximate Bayesian computation publication-title: Biometrika doi: 10.1093/biomet/asy027 – volume: 110 start-page: 1321 year: 2013 ident: 2023022101111891300_ article-title: Bayesian computation via empirical likelihood publication-title: Proc. Natn. Acad. Sci. USA doi: 10.1073/pnas.1208827110 – volume-title: Space-filling Curves year: 1994 ident: 2023022101111891300_ doi: 10.1007/978-1-4612-0871-6 – volume-title: On Bayesian inference for the M/G/1 queue with efficient MCMC sampling year: 2014 ident: 2023022101111891300_ – year: 2018 ident: 2023022101111891300_ article-title: Computational optimal transport publication-title: Foundns Trends Mach. Learn. – year: 2018 ident: 2023022101111891300_ article-title: Robust Bayesian inference via coarsening publication-title: J. Am. Statist. Ass. – start-page: 398 volume-title: Proc. 19th Int. Conf. Artificial Intelligence and Statistics year: 2016 ident: 2023022101111891300_ – volume-title: Optimal Transport for Applied Mathematicians year: 2015 ident: 2023022101111891300_ doi: 10.1007/978-3-319-20828-2 – volume: 7 start-page: 1632 year: 2013 ident: 2023022101111891300_ article-title: A simple approach to maximum intractable likelihood estimation publication-title: Electron. J. Statist. doi: 10.1214/13-EJS819 – volume-title: CGAL: User and Reference Manual year: 2016 ident: 2023022101111891300_ – volume-title: A rare event approach to high dimensional approximate Bayesian computation year: 2016 ident: 2023022101111891300_ – volume-title: transport: optimal transport in various forms year: 2017 ident: 2023022101111891300_ – volume: 22 start-page: 1009 year: 2012 ident: 2023022101111891300_ article-title: An adaptive sequential Monte Carlo method for approximate Bayesian computation publication-title: Statist. Comput. doi: 10.1007/s11222-011-9271-y – volume: 13 start-page: 519 year: 2003 ident: 2023022101111891300_ article-title: Delay embeddings for forced system: II, Stochastic forcing publication-title: J. Nonlin. Sci. doi: 10.1007/s00332-003-0534-4 – volume: 22 start-page: 919 year: 1994 ident: 2023022101111891300_ article-title: The transportation cost from the uniform measure to the empirical measure in dimension 3 publication-title: Ann. Probab. doi: 10.1214/aop/1176988735 – year: 2019 ident: 2023022101111891300_ article-title: Negative association, ordering and convergence of resampling methods publication-title: Ann. Statist doi: 10.1214/18-AOS1746 – volume: 101 start-page: 655 year: 2014 ident: 2023022101111891300_ article-title: Variance bounding and geometric ergodicity of Markov chain Monte Carlo kernels for approximate Bayesian computation publication-title: Biometrika doi: 10.1093/biomet/asu027 – volume: 81 start-page: 1805 year: 2013 ident: 2023022101111891300_ article-title: Risk of Bayesian inference in misspecified models, and the sandwich covariance matrix publication-title: Econometrica doi: 10.3982/ECTA9097 – volume: 181 start-page: 1507 year: 2009 ident: 2023022101111891300_ article-title: Approximate Bayesian computation without summary statistics: the case of admixture publication-title: Genetics doi: 10.1534/genetics.108.098129 – volume: 74 start-page: 419 year: 2012 ident: 2023022101111891300_ article-title: Constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation (with discussion) publication-title: J. R. Statist. Soc. doi: 10.1111/j.1467-9868.2011.01010.x – volume: 10 year: 2011 ident: 2023022101111891300_ article-title: Bayesian learning from marginal data in bionetwork models publication-title: Statist. Appl. Genet. Molec. Biol. doi: 10.2202/1544-6115.1684 – volume: 55 start-page: 2541 year: 2011 ident: 2023022101111891300_ article-title: Likelihood-free Bayesian estimation of multivariate quantile distributions publication-title: Computnl Statist. Data Anal. doi: 10.1016/j.csda.2011.03.019 – volume-title: Nonlinear Time Series Analysis year: 2004 ident: 2023022101111891300_ – volume-title: Topics in Optimal Transportation year: 2003 ident: 2023022101111891300_ doi: 10.1090/gsm/058 – volume: 72 start-page: 269 year: 2010 ident: 2023022101111891300_ article-title: Particle Markov chain Monte Carlo methods (with discussion) publication-title: J. R. Statist. Soc. doi: 10.1111/j.1467-9868.2009.00736.x – start-page: 304 volume-title: Proc. Winter Simulation Conf. (ed. O. Rose) year: 2012 ident: 2023022101111891300_ – volume: 102 start-page: 187 year: 1997 ident: 2023022101111891300_ article-title: Measuring the distance between time series publication-title: Physica – volume: 59 start-page: 187 year: 2017 ident: 2023022101111891300_ article-title: A transportation lp distance for signal analysis publication-title: J. Math. Imgng Visn doi: 10.1007/s10851-017-0726-4 – volume: 105 start-page: 285 year: 2018 ident: 2023022101111891300_ article-title: On the asymptotic efficiency of approximate Bayesian computation estimators publication-title: Biometrika doi: 10.1093/biomet/asx078 – start-page: 435 volume-title: Proc. Int. Conf. Scale Space and Variational Methods in Computer Vision year: 2011 ident: 2023022101111891300_ – volume: 51 start-page: 22 year: 2015 ident: 2023022101111891300_ article-title: Sliced and Radon Wasserstein barycenters of measures publication-title: J. Math. Imgng Visn doi: 10.1007/s10851-014-0506-3 – start-page: 199 volume-title: Proc. 18th Int. Conf. Hybrid Systems: Computation and Control year: 2015 ident: 2023022101111891300_ – volume: 451 start-page: 132 year: 2017 ident: 2023022101111891300_ article-title: An algorithm to approximate the optimal expected inner product of two vectors with given marginals publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2017.02.003 – volume: 19 year: 2017 ident: 2023022101111891300_ article-title: On Wasserstein two-sample testing and related families of nonparametric tests publication-title: Entropy doi: 10.3390/e19020047 – volume-title: Inference in generative models using the Wasserstein distance year: 2017 ident: 2023022101111891300_ – volume: 162 start-page: 707 year: 2015 ident: 2023022101111891300_ article-title: On the rate of convergence in Wasserstein distance of the empirical measure publication-title: Probab. Theory Reltd Flds doi: 10.1007/s00440-014-0583-7 – volume: 64 start-page: 253 year: 2002 ident: 2023022101111891300_ article-title: Econometric analysis of realized volatility and its use in estimating stochastic volatility models publication-title: J. R. Statist. Soc. doi: 10.1111/1467-9868.00336 – volume: 41 start-page: 2 year: 2008 ident: 2023022101111891300_ article-title: Computing the Fréchet distance between simple polygons publication-title: Computnl Geom. doi: 10.1016/j.comgeo.2007.08.003 – start-page: 1608 volume-title: Learning generative models with Sinkhorn divergences year: 2017 ident: 2023022101111891300_ – volume-title: Assignment Problems year: 2009 ident: 2023022101111891300_ doi: 10.1137/1.9780898717754 – year: 2018 ident: 2023022101111891300_ article-title: Statistical aspects of Wasserstein distances publication-title: A. Rev. Statist. Appl.
SSID	ssj0000673
Score	2.6133783
Snippet	A growing number of generative statistical models do not permit the numerical evaluation of their likelihood functions. Approximate Bayesian computation has... Summary A growing number of generative statistical models do not permit the numerical evaluation of their likelihood functions. Approximate Bayesian...
SourceID	proquest crossref wiley jstor
SourceType	Aggregation Database Enrichment Source Index Database Publisher
StartPage	235
SubjectTerms	Approximate Bayesian computation Bayesian analysis Bayesian theory Biology Computation Computer simulation Data data collection Datasets equations Generative models Hilbert curve Hilbert space Likelihood‐free inference Optimal transport Property Queueing Queues Regression analysis Statistical methods Statistical models Statistics Summaries Time series time series analysis Volatility Wasserstein distance
Title	Approximate Bayesian computation with the Wasserstein distance
URI	https://www.jstor.org/stable/26773210 https://onlinelibrary.wiley.com/doi/abs/10.1111%2Frssb.12312 https://www.proquest.com/docview/2193148291 https://www.proquest.com/docview/2237500962
Volume	81
WOSCitedRecordID	wos000461872300002&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVWIB databaseName: Wiley Online Library Full Collection 2020 customDbUrl: eissn: 1467-9868 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000673 issn: 1369-7412 databaseCode: DRFUL dateStart: 19970101 isFulltext: true titleUrlDefault: https://onlinelibrary.wiley.com providerName: Wiley-Blackwell
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3dS8MwED_G5sNe_B5Op1T0RaGyplm7gAibOnyQIZvDvZU0uYIgnWxO9L_3knZ1AxHEt0Kubch9_S7J3QGcapRSCJa4jKILl5PLcEVCMY9sYstTNNDmsW02Efb77fFYPJTgcpELk9WHKDbcjGZYe20UXMazJSWfzmbxBdld02K4wkhwW2Wo3Ax6o_tlS-xneVfCJc_J8vKk5ibP99srDim7k7iCNpcxq3U6vY3_TXcT1nOw6XQy6diCEqbbUDX4MivPvANXHVNT_OOZcCs6XfmJJqfSUbbVg-WZYzZqHUKJzpO0mZmmO6ajDeokcdmFUe_28frOzVsquMqcyLqCJ7oZe0nABfIAOWNCeyhFQlYOQ6a9pmoxzVBy0n3FpAh0wEIv9hEVxR6JX4NyOklxDxyJItZezGNfKi4pbiPfjz5R-ehp0uw6nC3WNVJ5vXHT9uIlWsQdZkkiuyR1OCloX7MqGz9S1Sx7ChIWhKHJQapDY8GvKFfBWUSm2DdFTgXN5LgYJuUxJyIyxcmcaJhPiImiOPr2ueXeL7-PBsNh1z7t_4X4AKoEskR226cB5bfpHA9hTb0Tq6dHuch-ASUA7z8
linkProvider	Wiley-Blackwell
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3dS8MwEA8yBffi93B-RvRFobKmsTUvwqaOiXPIPnBvJU2uIMiUTUX_e-_Sbm4ggvhWyLUNua_fJbk7xo4saK2USD2B0YUn0WV4KsWYR1fgzDc4cC4T12wiarXO-311n9_NoVyYrD7EZMONNMPZa1Jw2pCe0vLhaJScouGlHsPzEuUIBXz-ql3vNadNcZAlXikPXafI65PSVZ7vt2c8UnYpcQZuToNW53Xqy_-c7wpbyuEmr2byscrmYLDGioQwswLN6-yiSlXFPx4RuQKv6U-grEpuXLMHxzVOW7UccSJ_0C43k_pjcku4EwVmg_Xq193Lhpc3VfAMncl6Sqa2kvhpKBXIEKQQyvqgVYp2DiJh_Yo5E1aAlqj9RmgV2lBEfhIAGIw-0qDECoPnAWwyrkEl1k9kEmgjNUZu6P0hQKoAfIu6XWbH44WNTV5xnBpfPMXjyIOWJHZLUmaHE9qXrM7Gj1Qlx58JiQijiLKQymxnzLA4V8JRjMY4oDKnCmdyMBlG9aEzET2A5zekEQFiJozj8Nsnjn2__D5udzo197T1F-J9ttjo3jXj5k3rdpsVEXKp7O7PDiu8Dt9gly2Yd2T7cC-X3y93-fMv
linkToPdf	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3dS8MwED9kiuzF7-H8rOiLQmVNY2teBL-G4hiiDvdW0uQKgnSyqeh_713azQ1EEN8KubYhl7v7XXIfAHsWtVZKZL4g78KXZDJ8lZHPoxt4FBgaOJapazYRt9vH3a66LWNzOBemqA8xOnBjyXD6mgUcX2w2JuX9wSA9JMXLPYanJXeRqcD0xV2z0xpXxWGReKV8Mp2irE_KoTzfb09YpCIocQJujoNWZ3Wa8_-c7wLMlXDTOy32xyJMYb4EVUaYRYHmZTg55ariH0-EXNE705_IWZWecc0eHNc8Pqr1CCd6j9rlZnJ_TM8y7qQNswKd5uXD-ZVfNlXwDd_J-kpmtpEGWSQVygilEMoGqFVGeg5jYYOGORJWoJYk_UZoFdlIxEEaIhryPrKwBpW8l-MqeBpVaoNUpqE2UpPnRtYfQ6IKMbAk23XYHy5sYsqK49z44jkZeh68JIlbkjrsjmhfijobP1LVHH9GJCKKY85CqsPGkGFJKYSDhJRxyGVOFc1kZzRM4sN3IjrH3hvRiJAwE_lx9O0Dx75ffp_c3d-fuae1vxBvw-ztRTNpXbdv1qFKiEsVoT8bUHntv-EmzJh34np_q9y-XxZ48qo
openUrl	ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Approximate+Bayesian+computation+with+the+Wasserstein+distance&rft.jtitle=Journal+of+the+Royal+Statistical+Society.+Series+B%2C+Statistical+methodology&rft.au=Bernton%2C+Espen&rft.au=Jacob%2C+Pierre+E.&rft.au=Gerber%2C+Mathieu&rft.au=Robert%2C+Christian+P.&rft.date=2019-04-01&rft.pub=Wiley&rft.issn=1369-7412&rft.eissn=1467-9868&rft.volume=81&rft.issue=2&rft.spage=235&rft.epage=269&rft_id=info:doi/10.1111%2Frssb.12312&rft.externalDocID=26773210
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1369-7412&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1369-7412&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1369-7412&client=summon