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...

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Vydáno v:	Journal of the Royal Statistical Society. Series B, Statistical methodology Ročník 81; číslo 2; s. 235 - 269
Hlavní autoři:	Bernton, Espen, Jacob, Pierre E., Gerber, Mathieu, Robert, Christian P.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Oxford Wiley 01.04.2019 Oxford University Press
Témata:	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
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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	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. 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.
Author	Robert, Christian P. Gerber, Mathieu Jacob, Pierre E. Bernton, Espen
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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
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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.
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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...
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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
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