Edit Profile (opens in new tab) Stuart, Andrew M. Compute Distance To: Compute Author ID: stuart.andrew-m Published as: Stuart, A. M.; Stuart, Andrew M.; Stuart, Andrew; Stuart, A. External Links: MGP · Wikidata · IdRef Documents Indexed: 193 Publications since 1987, including 5 Books 3 Contributions as Editor · 1 Further Contribution Reviewing Activity: 5 Reviews Co-Authors: 151 Co-Authors with 178 Joint Publications 4,539 Co-Co-Authors all top 5 Co-Authors 16 single-authored 13 Pavliotis, Grigorios A. 10 Law, Kody J. H. 10 Voss, Jochen 9 Beskos, Alexandros 8 Dunlop, Matthew M. 8 Hairer, Martin 7 Humphries, Antony R. 7 Iglesias, Marco A. 7 Norbury, John W. 7 Roberts, Gareth O. 6 Dashti, Masoumeh 6 Higham, Desmond J. 6 Pillai, Natesh S. 6 Zygalakis, Konstantinos C. 5 Elliott, Charles M. 5 Hosseini, Bamdad 5 Mattingly, Jonathan Christopher 5 Pinski, Frank J. 5 Pokern, Yvo 5 Sanz-Serna, Jesús María 4 Agapiou, Sergios 4 Cotter, Simon L. 4 Girolami, Mark A. 4 Papaspiliopoulos, Omiros 4 Sanz-Alonso, Daniel 4 Sigurgeirsson, Hersir 4 Weber, Hendrik 3 Bai, Fengshan 3 Budd, Christopher John 3 Hoang, Viet Ha 3 Hoffmann, Franca 3 Jones, Don A. 3 Kovachki, Nikola B. 3 Lamba, Harbir 3 Lu, Yulong 3 Ottobre, Michela 3 Spence, Alastair 3 Teckentrup, Aretha L. 3 Thiéry, Alexandre H. 3 Wiberg, Petter 2 Apte, Amit 2 Bertozzi, Andrea Louise 2 Cano, Begoña 2 Chada, Neil K. 2 Chaplain, Mark A. J. 2 Chen, Yifan 2 Estep, Donald J. 2 Fearnhead, Paul 2 Garbuno-Inigo, Alfredo 2 Griewank, Andreas 2 Iserles, Arieh 2 Jasra, Ajay 2 Kelly, David Thomas Bryant 2 Kuntz, Juan 2 Kupferman, Raz 2 Lan, Shiwei 2 Lee, Wonjung 2 Lin, Kui 2 Mao, Xuerong 2 Owhadi, Houman 2 Peplow, Andrew T. 2 Reich, Sebastian 2 Roulstone, Ian 2 Schillings, Claudia 2 Schneider, Tapio 2 Schwab, Christoph 2 Shukla, Abhishek Kumar 2 Warren, J. O. 2 Wolfram, Marie-Therese 1 Adams, Ryan Prescott 1 Albers, David J. 1 Anaya-Izquierdo, Karim Alejandro 1 Archambeau, Cédric 1 Band, Leah R. 1 Bardsley, Johnathan M. 1 Barkley, Dwight 1 Barthelmé, Simon 1 Beffy, Magali 1 Bhadra, Anindya 1 Bjørhus, Morten 1 Blancquart, Paul-Adrien 1 Blömker, Dirk 1 Bornn, Luke 1 Bouchard, Guillaume 1 Bourguignon, Jean-Pierre 1 Boys, Richard J. 1 Bréhier, Charles-Edouard 1 Brett, C. E. A. 1 Bühlmann, Peter 1 Burov, Dmitry A. 1 Calderhead, Ben 1 Calvetti, Daniela 1 Campbell, David A. 1 Cao, Jiguo 1 Chen, Yanjiun 1 Chin, Siu A. 1 Chopin, Nicolas 1 Christie, Mike 1 Cleary, Emmet 1 Conrad, Patrick R. ...and 129 more Co-Authors all top 5 Serials 13 Inverse Problems 12 SIAM Journal on Numerical Analysis 8 SIAM Journal on Applied Mathematics 6 Journal of Computational Physics 6 Physica D 6 The Annals of Applied Probability 6 Communications in Mathematical Sciences 5 IMA Journal of Numerical Analysis 5 Nonlinearity 5 Stochastic Processes and their Applications 5 SIAM Journal on Scientific Computing 5 Multiscale Modeling & Simulation 5 SIAM/ASA Journal on Uncertainty Quantification 4 IMA Journal of Applied Mathematics 4 Mathematics of Computation 4 Statistics and Computing 3 Journal of Statistical Physics 3 Journal of Differential Equations 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 Journal of the Royal Statistical Society. Series B. Statistical Methodology 3 Journal of Machine Learning Research (JMLR) 3 Stochastics and Dynamics 3 SIAM Journal on Applied Dynamical Systems 3 Oberwolfach Reports 3 Stochastic and Partial Differential Equations. Analysis and Computations 2 International Journal for Numerical Methods in Fluids 2 Rocky Mountain Journal of Mathematics 2 BIT 2 Statistical Science 2 IMA Journal of Mathematics Applied in Medicine and Biology 2 SIAM Journal on Mathematical Analysis 2 SIAM Review 2 Applied and Computational Harmonic Analysis 2 Bernoulli 2 Texts in Applied Mathematics 2 Cambridge Monographs on Applied and Computational Mathematics 2 Inverse Problems and Imaging 2 SMAI Journal of Computational Mathematics 1 Applicable Analysis 1 Communications on Pure and Applied Mathematics 1 Journal of Mathematical Analysis and Applications 1 Quarterly Journal of Mechanics and Applied Mathematics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Biometrika 1 Numerical Functional Analysis and Optimization 1 SIAM Journal on Scientific and Statistical Computing 1 Chinese Annals of Mathematics. Series B 1 Journal of Computational Mathematics 1 European Journal of Applied Mathematics 1 Numerical Algorithms 1 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 1 Journal of Nonlinear Science 1 Physics of Fluids 1 Journal of Inverse and Ill-Posed Problems 1 Discrete and Continuous Dynamical Systems 1 European Mathematical Society Newsletter 1 Markov Processes and Related Fields 1 Interfaces and Free Boundaries 1 LMS Journal of Computation and Mathematics 1 Computational Geosciences 1 Foundations of Computational Mathematics 1 Acta Numerica 1 Transactions of Mathematics and its Applications 1 Cambridge Texts in Applied Mathematics all top 5 Fields 109 Numerical analysis (65-XX) 74 Probability theory and stochastic processes (60-XX) 66 Statistics (62-XX) 62 Partial differential equations (35-XX) 34 Dynamical systems and ergodic theory (37-XX) 30 Ordinary differential equations (34-XX) 17 Fluid mechanics (76-XX) 15 Statistical mechanics, structure of matter (82-XX) 12 Computer science (68-XX) 12 Systems theory; control (93-XX) 6 Integral equations (45-XX) 6 Operator theory (47-XX) 6 Biology and other natural sciences (92-XX) 5 Functional analysis (46-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 5 Classical thermodynamics, heat transfer (80-XX) 5 Information and communication theory, circuits (94-XX) 4 Mechanics of particles and systems (70-XX) 4 Geophysics (86-XX) 3 General and overarching topics; collections (00-XX) 3 Measure and integration (28-XX) 3 Operations research, mathematical programming (90-XX) 2 Combinatorics (05-XX) 2 Real functions (26-XX) 2 Mechanics of deformable solids (74-XX) 1 History and biography (01-XX) 1 Approximations and expansions (41-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Optics, electromagnetic theory (78-XX) 1 Quantum theory (81-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 177 Publications have been cited 4,755 times in 2,766 Documents Cited by ▼ Year ▼ Inverse problems: a Bayesian perspective. Zbl 1242.65142Stuart, A. M. 395 2010 Strong convergence of Euler-type methods for nonlinear stochastic differential equations. Zbl 1026.65003Higham, Desmond J.; Mao, Xuerong; Stuart, Andrew M. 282 2002 Multiscale methods. Averaging and homogenization. Zbl 1160.35006Pavliotis, Grigorios A.; Stuart, Andrew M. 240 2008 Dynamical systems and numerical analysis. Zbl 0869.65043Stuart, A. M.; Humphries, A. R. 232 1996 Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise. Zbl 1075.60072Mattingly, J. C.; Stuart, A. M.; Higham, D. J. 175 2002 MCMC methods for functions: modifying old algorithms to make them faster. Zbl 1331.62132Cotter, S. L.; Roberts, G. O.; Stuart, A. M.; White, D. 143 2013 Riemann manifold Langevin and Hamiltonian Monte Carlo methods. With discussion and authors’ reply. Zbl 1411.62071Girolami, Mark; Calderhead, Ben 129 2011 The global dynamics of discrete semilinear parabolic equations. Zbl 0792.65066Elliott, C. M.; Stuart, A. M. 109 1993 Data assimilation. A mathematical introduction. Zbl 1353.60002Law, Kody; Stuart, Andrew; Zygalakis, Konstantinos 106 2015 Dynamical systems and numerical analysis. Zbl 0913.65068Stuart, A. M.; Humphries, A. R. 93 1998 Extracting macroscopic dynamics: model problems and algorithms. Zbl 1073.82038Givon, Dror; Kupferman, Raz; Stuart, Andrew 92 2004 Exponential mean-square stability of numerical solutions to stochastic differential equations. Zbl 1055.65009Higham, Desmond J.; Mao, Xuerong; Stuart, Andrew M. 74 2003 A model mechanism for the chemotactic response of endothelial cells to tumour angiogenesis factor. Zbl 0783.92019Chaplain, M. A. J.; Stuart, A. M. 70 1993 Viscous Cahn-Hilliard equation. II: Analysis. Zbl 0855.35067Elliott, C. M.; Stuart, A. M. 64 1996 Ensemble Kalman methods for inverse problems. Zbl 1311.65064Iglesias, Marco A.; Law, Kody J. H.; Stuart, Andrew M. 64 2013 Runge-Kutta methods for dissipative and gradient dynamical systems. Zbl 0807.34057Humphries, A. R.; Stuart, A. M. 61 1994 Space-time continuous analysis of waveform relaxation for the heat equation. Zbl 0911.65082Gander, Martin J.; Stuart, Andrew M. 57 1998 MAP estimators and their consistency in Bayesian nonparametric inverse problems. Zbl 1281.62089Dashti, M.; Law, K. J. H.; Stuart, A. M.; Voss, J. 56 2013 Optimal tuning of the hybrid Monte Carlo algorithm. Zbl 1287.60090Beskos, Alexandros; Pillai, Natesh; Roberts, Gareth; Sanz-Serna, Jesus-Maria; Stuart, Andrew 52 2013 MCMC methods for diffusion bridges. Zbl 1159.65007Beskos, Alexandros; Roberts, Gareth; Stuart, Andrew; Voss, Jochen 52 2008 Spectral gaps for a Metropolis-Hastings algorithm in infinite dimensions. Zbl 1307.65002Hairer, Martin; Stuart, Andrew M.; Vollmer, Sebastian J. 51 2014 The viscous Cahn-Hilliard equation. I: Computations. Zbl 0818.35045Bai, F.; Elliott, C. M.; Gardiner, A.; Spence, A.; Stuart, A. M. 51 1995 Analysis of the ensemble Kalman filter for inverse problems. Zbl 1366.65101Schillings, Claudia; Stuart, Andrew M. 51 2017 Analysis of SPDEs arising in path sampling. II: The nonlinear case. Zbl 1140.60329Hairer, M.; Stuart, A. M.; Voss, J. 41 2007 Sparse deterministic approximation of Bayesian inverse problems. Zbl 1236.62014Schwab, C.; Stuart, A. M. 40 2012 Diffusion limits of the random walk Metropolis algorithm in high dimensions. Zbl 1254.60081Mattingly, Jonathan C.; Pillai, Natesh S.; Stuart, Andrew M. 40 2012 Optimal scalings for local Metropolis-Hastings chains on nonproduct targets in high dimensions. Zbl 1172.60328Beskos, Alexandros; Roberts, Gareth; Stuart, Andrew 39 2009 Uncertainty quantification and weak approximation of an elliptic inverse problem. Zbl 1234.35309Dashti, M.; Stuart, A. M. 37 2011 Complexity analysis of accelerated MCMC methods for Bayesian inversion. Zbl 1288.65004Hoang, Viet Ha; Schwab, Christoph; Stuart, Andrew M. 36 2013 Convergence of numerical time-averaging and stationary measures via Poisson equations. Zbl 1217.65014Mattingly, Jonathan C.; Stuart, Andrew M.; Tretyakov, M. V. 35 2010 Posterior contraction rates for the Bayesian approach to linear ill-posed inverse problems. Zbl 1284.62289Agapiou, Sergios; Larsson, Stig; Stuart, Andrew M. 35 2013 Model problems in numerical stability theory for initial value problems. Zbl 0807.65091Stuart, A. M.; Humphries, A. R. 34 1994 Blow-up in a partial differential equation with conserved first integral. Zbl 0784.35009Budd, Chris; Dold, Bill; Stuart, Andrew 32 1993 Approximation of Bayesian inverse problems for PDEs. Zbl 1210.35284Cotter, S. L.; Dashti, M.; Stuart, A. M. 32 2010 Well-posedness and accuracy of the ensemble Kalman filter in discrete and continuous time. Zbl 1305.62323Kelly, D. T. B.; Law, K. J. H.; Stuart, A. M. 31 2014 Besov priors for Bayesian inverse problems. Zbl 1243.62032Dashti, Masoumeh; Harris, Stephen; Stuart, Andrew 31 2012 Optimal scaling and diffusion limits for the Langevin algorithm in high dimensions. Zbl 1272.60053Pillai, Natesh S.; Stuart, Andrew M.; Thiéry, Alexandre H. 31 2012 Parameter estimation for multiscale diffusions. Zbl 1137.82016Pavliotis, G. A.; Stuart, A. M. 31 2007 Posterior consistency for Gaussian process approximations of Bayesian posterior distributions. Zbl 1429.60040Stuart, Andrew M.; Teckentrup, Aretha L. 30 2018 Importance sampling: intrinsic dimension and computational cost. Zbl 1442.62026Agapiou, S.; Papaspiliopoulos, O.; Sanz-Alonso, D.; Stuart, A. M. 30 2017 Hybrid Monte Carlo on Hilbert spaces. Zbl 1235.60091Beskos, A.; Pinski, F. J.; Sanz-Serna, J. M.; Stuart, A. M. 30 2011 A first course in continuum mechanics. Zbl 1143.74001Gonzalez, Oscar; Stuart, Andrew M. 29 2008 Geometric MCMC for infinite-dimensional inverse problems. Zbl 1375.35627Beskos, Alexandros; Girolami, Mark; Lan, Shiwei; Farrell, Patrick E.; Stuart, Andrew M. 28 2017 Analysis of SPDEs arising in path sampling. I: The Gaussian case. Zbl 1138.60326Hairer, M.; Stuart, A. M.; Voss, J.; Wiberg, P. 28 2005 A note on diffusion limits of chaotic skew-product flows. Zbl 1220.37009Melbourne, I.; Stuart, A. M. 28 2011 Hierarchical Bayesian level set inversion. Zbl 1384.62084Dunlop, Matthew M.; Iglesias, Marco A.; Stuart, Andrew M. 26 2017 Bayesian inverse problems for functions and applications to fluid mechanics. Zbl 1228.35269Cotter, S. L.; Dashti, M.; Robinson, J. C.; Stuart, A. M. 26 2009 An adaptive Euler-Maruyama scheme for SDEs: Convergence and stability. Zbl 1127.65005Lamba, H.; Mattingly, J. C.; Stuart, A. M. 26 2007 Accuracy and stability of the continuous-time 3DVAR filter for the Navier-Stokes equation. Zbl 1271.34013Blömker, D.; Law, K.; Stuart, A. M.; Zygalakis, K. C. 25 2013 Sampling the posterior: an approach to non-Gaussian data assimilation. Zbl 1113.62026Apte, A.; Hairer, M.; Stuart, A. M.; Voss, J. 25 2007 Numerical wave propagation in an advection equation with a nonlinear source term. Zbl 0759.65060Griffiths, D. F.; Stuart, A. M.; Yee, H. C. 24 1992 A perturbation theory for ergodic Markov chains and application to numerical approximations. Zbl 0961.60068Shardlow, T.; Stuart, A. M. 24 2000 Uncertainty quantification in graph-based classification of high dimensional data. Zbl 1394.62083Bertozzi, Andrea L.; Luo, Xiyang; Stuart, Andrew M.; Zygalakis, Konstantinos C. 23 2018 On the computation of blow-up. Zbl 0701.76038Stuart, A. M.; Floater, M. S. 23 1990 Evaluation of Gaussian approximations for data assimilation in reservoir models. Zbl 1393.86020Iglesias, Marco A.; Law, Kody J. H.; Stuart, Andrew M. 22 2013 Conditional path sampling of SDEs and the Langevin MCMC method. Zbl 1082.65004Stuart, Andrew M.; Voss, Jochen; Wiberg, Petter 22 2004 Sequential Monte Carlo methods for Bayesian elliptic inverse problems. Zbl 1331.65012Beskos, Alexandros; Jasra, Ajay; Muzaffer, Ege A.; Stuart, Andrew M. 22 2015 Maximum likelihood drift estimation for multiscale diffusions. Zbl 1171.62047Papavasiliou, A.; Pavliotis, G. A.; Stuart, A. M. 22 2009 Statistical analysis of differential equations: introducing probability measures on numerical solutions. Zbl 1384.62082Conrad, Patrick R.; Girolami, Mark; Särkkä, Simo; Stuart, Andrew; Zygalakis, Konstantinos 21 2017 Geometric ergodicity of some hypo-elliptic diffusions for particle motions. Zbl 1014.60059Mattingly, J. C.; Stuart, A. M. 20 2002 A Bayesian level set method for geometric inverse problems. Zbl 1353.65050Iglesias, Marco A.; Lu, Yulong; Stuart, Andrew M. 20 2016 Parameter estimation for partially observed hypoelliptic diffusions. Zbl 1231.62152Pokern, Yvo; Stuart, Andrew M.; Wiberg, Petter 20 2009 Parameterizations for ensemble Kalman inversion. Zbl 06897207Chada, Neil K.; Iglesias, Marco A.; Roininen, Lassi; Stuart, Andrew M. 20 2018 Interacting Langevin diffusions: gradient structure and ensemble Kalman sampler. Zbl 1447.65119Garbuno-Inigo, Alfredo; Hoffmann, Franca; Li, Wuchen; Stuart, Andrew M. 20 2020 Analysis of the Gibbs sampler for hierarchical inverse problems. Zbl 1308.62097Agapiou, Sergios; Bardsley, Johnathan M.; Papaspiliopoulos, Omiros; Stuart, Andrew M. 19 2014 Convergence analysis of ensemble Kalman inversion: the linear, noisy case. Zbl 1448.65209Schillings, C.; Stuart, A. M. 19 2018 A unified approach to spurious solutions introduced by time discretization. I: Basic theory. Zbl 0736.65050Iserles, A.; Peplow, A. T.; Stuart, A. M. 19 1991 Well-posed Bayesian geometric inverse problems arising in subsurface flow. Zbl 1304.35767Iglesias, Marco A.; Lin, Kui; Stuart, Andrew M. 18 2014 Ergodicity of dissipative differential equations subject to random impulses. Zbl 0934.34047Sanz-Serna, J. M.; Stuart, A. M. 18 1999 Nonparametric estimation of diffusions: a differential equations approach. Zbl 1437.62575Papaspiliopoulos, Omiros; Pokern, Yvo; Roberts, Gareth O.; Stuart, Andrew M. 18 2012 A model for preferential concentration. Zbl 1185.76341Sigurgeirsson, H.; Stuart, A. M. 18 2002 Kullback-Leibler approximation for probability measures on infinite dimensional spaces. Zbl 1342.60049Pinski, F. J.; Simpson, G.; Stuart, A. M.; Weber, H. 18 2015 White noise limits for inertial particles in a random field. Zbl 1038.60060Pavliotis, G. A.; Stuart, A. M. 17 2003 Algorithms for particle-field simulations with collisions. Zbl 1158.82300Sigurgeirsson, Hersir; Stuart, Andrew; Wan, Wing-Lok 17 2001 The Bayesian formulation of EIT: analysis and algorithms. Zbl 1348.62104Dunlop, Matthew M.; Stuart, Andrew M. 17 2016 Algorithms for Kullback-Leibler approximation of probability measures in infinite dimensions. Zbl 1348.60033Pinski, F. J.; Simpson, G.; Stuart, A. M.; Weber, H. 17 2015 Quasi-Monte Carlo and multilevel Monte Carlo methods for computing posterior expectations in elliptic inverse problems. Zbl 06736512Scheichl, R.; Stuart, A. M.; Teckentrup, A. L. 17 2017 Numerical analysis of dynamical systems. Zbl 0809.65076Stuart, Andrew M. 16 1994 A function space HMC algorithm with second order Langevin diffusion limit. Zbl 1346.60119Ottobre, Michela; Pillai, Natesh S.; Pinski, Frank J.; Stuart, Andrew M. 16 2016 How deep are deep Gaussian processes? Zbl 1469.60107Dunlop, Matthew M.; Girolami, Mark A.; Stuart, Andrew M.; Teckentrup, Aretha L. 14 2018 Iterative updating of model error for Bayesian inversion. Zbl 1386.65056Calvetti, Daniela; Dunlop, Matthew; Somersalo, Erkki; Stuart, Andrew 14 2018 Analysis of the 3DVAR filter for the partially observed Lorenz ’63 model. Zbl 1283.62194Law, Kody; Shukla, Abhishek; Stuart, Andrew 14 2014 Signal processing problems on function space: Bayesian formulation, stochastic PDEs and effective MCMC methods. Zbl 1262.94012Hairer, M.; Stuart, A.; Voss, J. 14 2011 The numerical computation of heteroclinic connections in systems of gradient partial differential equations. Zbl 0786.65077Bai, Fengshan; Spence, Alastair; Stuart, Andrew M. 14 1993 Long-term behaviour of large mechanical systems with random initial data. Zbl 1032.70009Kupperman, R.; Stuart, A. M.; Terry, J. R.; Tupper, P. F. 13 2002 A model for a porous-medium combustion. Zbl 0679.76104Norbury, J.; Stuart, A. M. 13 1989 Bayesian posterior contraction rates for linear severely ill-posed inverse problems. Zbl 1288.62036Agapiou, Sergios; Stuart, Andrew M.; Zhang, Yuan-Xiang 13 2014 Data assimilation: mathematical and statistical perspectives. Zbl 1384.62300Apte, A.; Jones, C. K. R. T.; Stuart, A. M.; Voss, J. 13 2008 Ensemble Kalman inversion: a derivative-free technique for machine learning tasks. Zbl 1430.68266Kovachki, Nikola B.; Stuart, Andrew M. 12 2019 Posterior consistency via precision operators for Bayesian nonparametric drift estimation in SDEs. Zbl 1256.62047Pokern, Y.; Stuart, A. M.; van Zanten, J. H. 12 2013 MCMC methods for sampling function space. Zbl 1179.65003Beskos, Alexandros; Stuart, Andrew 12 2008 Volterra integral equations and a new Gronwall inequality. I: The linear case. Zbl 0639.65075Norbury, J.; Stuart, A. M. 12 1987 MAP estimators for piecewise continuous inversion. Zbl 1354.65112Dunlop, M. M.; Stuart, A. M. 12 2016 Volterra integral equations and a new Gronwall inequality. II: The nonlinear case. Zbl 0639.65076Norbury, J.; Stuart, A. M. 11 1987 Travelling combustion waves in porous medium. I. Existence. Zbl 0642.34013Norbury, J.; Stuart, A. M. 11 1988 Blow-up in a system of partial differential equations with conserved first integral. II: Problems with convection. Zbl 0928.35081Budd, C. J.; Dold, J. W.; Stuart, A. M. 11 1994 Accuracy and stability of filters for dissipative PDEs. Zbl 1350.65102Brett, C. E. A.; Lam, K. F.; Law, K. J. H.; McCormick, D. S.; Scott, M. R.; Stuart, A. M. 11 2013 The dynamical behavior of the discontinuous Galerkin method and related difference schemes. Zbl 0998.65080Estep, Donald J.; Stuart, Andrew M. 10 2002 Parabolic free boundary problems arising in porous medium combustion. Zbl 0681.35044Norbury, J.; Stuart, A. M. 10 1987 Filter accuracy for the Lorenz 96 model: fixed versus adaptive observation operators. Zbl 1364.93343Law, K. J. H.; Sanz-Alonso, D.; Shukla, A.; Stuart, A. M. 10 2016 Model reduction and neural networks for parametric PDEs. Zbl 1481.65260Bhattacharya, Kaushik; Hosseini, Bamdad; Kovachki, Nikola B.; Stuart, Andrew M. 5 2021 Consistency of empirical Bayes and kernel flow for hierarchical parameter estimation. Zbl 1472.62012Chen, Yifan; Owhadi, Houman; Stuart, Andrew M. 2 2021 Kernel analog forecasting: multiscale test problems. Zbl 07382142Burov, Dmitry; Giannakis, Dimitrios; Manohar, Krithika; Stuart, Andrew 1 2021 Interacting Langevin diffusions: gradient structure and ensemble Kalman sampler. Zbl 1447.65119Garbuno-Inigo, Alfredo; Hoffmann, Franca; Li, Wuchen; Stuart, Andrew M. 20 2020 Large data and zero noise limits of graph-based semi-supervised learning algorithms. Zbl 1442.62768Dunlop, Matthew M.; Slepčev, Dejan; Stuart, Andrew M.; Thorpe, Matthew 8 2020 Tikhonov regularization within ensemble Kalman inversion. Zbl 1447.35337Chada, Neil K.; Stuart, Andrew M.; Tong, Xin T. 6 2020 Hyperparameter estimation in Bayesian MAP estimation: parameterizations and consistency. Zbl 1441.62084Dunlop, Matthew M.; Helin, Tapio; Stuart, Andrew M. 3 2020 Consistency of semi-supervised learning algorithms on graphs: probit and one-hot methods. Zbl 07306882Hoffmann, Franca; Hosseini, Bamdad; Ren, Zhi; Stuart, Andrew M. 2 2020 Reconciling Bayesian and perimeter regularization for binary inversion. Zbl 1455.62084Dunbar, Oliver R. A.; Dunlop, Matthew M.; Elliott, Charles M.; Hoang, Viet Ha; Stuart, Andrew M. 1 2020 Inverse optimal transport. Zbl 1434.90092Stuart, Andrew M.; Wolfram, Marie-Therese 1 2020 Ensemble Kalman inversion: a derivative-free technique for machine learning tasks. Zbl 1430.68266Kovachki, Nikola B.; Stuart, Andrew M. 12 2019 Strong convergence rates of probabilistic integrators for ordinary differential equations. Zbl 1431.65122Lie, Han Cheng; Stuart, A. M.; Sullivan, T. J. 8 2019 Parameter estimation for macroscopic pedestrian dynamics models from microscopic data. Zbl 1420.35112Gomes, Susana N.; Stuart, Andrew M.; Wolfram, Marie-Therese 6 2019 Ensemble Kalman methods with constraints. Zbl 1422.93173Albers, David J.; Blancquart, Paul-Adrien; Levine, Matthew E.; Esmaeilzadeh Seylabi, Elnaz; Stuart, Andrew 5 2019 Diffusion limit for the random walk Metropolis algorithm out of stationarity. Zbl 1467.60056Kuntz, Juan; Ottobre, Michela; Stuart, Andrew M. 5 2019 Posterior consistency for Gaussian process approximations of Bayesian posterior distributions. Zbl 1429.60040Stuart, Andrew M.; Teckentrup, Aretha L. 30 2018 Uncertainty quantification in graph-based classification of high dimensional data. Zbl 1394.62083Bertozzi, Andrea L.; Luo, Xiyang; Stuart, Andrew M.; Zygalakis, Konstantinos C. 23 2018 Parameterizations for ensemble Kalman inversion. Zbl 06897207Chada, Neil K.; Iglesias, Marco A.; Roininen, Lassi; Stuart, Andrew M. 20 2018 Convergence analysis of ensemble Kalman inversion: the linear, noisy case. Zbl 1448.65209Schillings, C.; Stuart, A. M. 19 2018 How deep are deep Gaussian processes? Zbl 1469.60107Dunlop, Matthew M.; Girolami, Mark A.; Stuart, Andrew M.; Teckentrup, Aretha L. 14 2018 Iterative updating of model error for Bayesian inversion. Zbl 1386.65056Calvetti, Daniela; Dunlop, Matthew; Somersalo, Erkki; Stuart, Andrew 14 2018 Weak error estimates for trajectories of SPDEs under spectral Galerkin discretization. Zbl 1413.65008Brehier, Charles Edouard; Hairer, Martin; Stuart, Andrew M. 5 2018 Non-stationary phase of the MALA algorithm. Zbl 1415.60091Kuntz, Juan; Ottobre, Michela; Stuart, Andrew M. 4 2018 Analysis of the ensemble Kalman filter for inverse problems. Zbl 1366.65101Schillings, Claudia; Stuart, Andrew M. 51 2017 Importance sampling: intrinsic dimension and computational cost. Zbl 1442.62026Agapiou, S.; Papaspiliopoulos, O.; Sanz-Alonso, D.; Stuart, A. M. 30 2017 Geometric MCMC for infinite-dimensional inverse problems. Zbl 1375.35627Beskos, Alexandros; Girolami, Mark; Lan, Shiwei; Farrell, Patrick E.; Stuart, Andrew M. 28 2017 Hierarchical Bayesian level set inversion. Zbl 1384.62084Dunlop, Matthew M.; Iglesias, Marco A.; Stuart, Andrew M. 26 2017 Statistical analysis of differential equations: introducing probability measures on numerical solutions. Zbl 1384.62082Conrad, Patrick R.; Girolami, Mark; Särkkä, Simo; Stuart, Andrew; Zygalakis, Konstantinos 21 2017 Quasi-Monte Carlo and multilevel Monte Carlo methods for computing posterior expectations in elliptic inverse problems. Zbl 06736512Scheichl, R.; Stuart, A. M.; Teckentrup, A. L. 17 2017 Gaussian approximations for probability measures on \(\mathbb R^d\). Zbl 1390.60022Lu, Yulong; Stuart, Andrew; Weber, Hendrik 6 2017 Gaussian approximations for transition paths in Brownian dynamics. Zbl 1375.60081Lu, Yulong; Stuart, Andrew; Weber, Hendrik 6 2017 Filter based methods for statistical linear inverse problems. Zbl 1383.93086Iglesias, Marco A.; Lin, Kui; Lu, Shuai; Stuart, Andrew M. 4 2017 Gaussian approximations of small noise diffusions in Kullback-Leibler divergence. Zbl 1384.28018Sanz-Alonso, Daniel; Stuart, Andrew M. 3 2017 Derivation and analysis of simplified filters. Zbl 1365.60042Lee, Wonjung; Stuart, Andrew 3 2017 A Bayesian level set method for geometric inverse problems. Zbl 1353.65050Iglesias, Marco A.; Lu, Yulong; Stuart, Andrew M. 20 2016 The Bayesian formulation of EIT: analysis and algorithms. Zbl 1348.62104Dunlop, Matthew M.; Stuart, Andrew M. 17 2016 A function space HMC algorithm with second order Langevin diffusion limit. Zbl 1346.60119Ottobre, Michela; Pillai, Natesh S.; Pinski, Frank J.; Stuart, Andrew M. 16 2016 MAP estimators for piecewise continuous inversion. Zbl 1354.65112Dunlop, M. M.; Stuart, A. M. 12 2016 Filter accuracy for the Lorenz 96 model: fixed versus adaptive observation operators. Zbl 1364.93343Law, K. J. H.; Sanz-Alonso, D.; Shukla, A.; Stuart, A. M. 10 2016 Mathematical and algorithmic aspects of data assimilation in the geosciences. Abstracts from the workshop held October 2–8, 2016. Zbl 1390.00096 1 2016 Data assimilation. A mathematical introduction. Zbl 1353.60002Law, Kody; Stuart, Andrew; Zygalakis, Konstantinos 106 2015 Sequential Monte Carlo methods for Bayesian elliptic inverse problems. Zbl 1331.65012Beskos, Alexandros; Jasra, Ajay; Muzaffer, Ege A.; Stuart, Andrew M. 22 2015 Kullback-Leibler approximation for probability measures on infinite dimensional spaces. Zbl 1342.60049Pinski, F. J.; Simpson, G.; Stuart, A. M.; Weber, H. 18 2015 Algorithms for Kullback-Leibler approximation of probability measures in infinite dimensions. Zbl 1348.60033Pinski, F. J.; Simpson, G.; Stuart, A. M.; Weber, H. 17 2015 Long-time asymptotics of the filtering distribution for partially observed chaotic dynamical systems. Zbl 1337.93094Sanz-Alonso, Daniel; Stuart, Andrew M. 8 2015 A multiscale analysis of diffusions on rapidly varying surfaces. Zbl 1311.35324Duncan, A. B.; Elliott, C. M.; Pavliotis, G. A.; Stuart, A. M. 2 2015 Spectral gaps for a Metropolis-Hastings algorithm in infinite dimensions. Zbl 1307.65002Hairer, Martin; Stuart, Andrew M.; Vollmer, Sebastian J. 51 2014 Well-posedness and accuracy of the ensemble Kalman filter in discrete and continuous time. Zbl 1305.62323Kelly, D. T. B.; Law, K. J. H.; Stuart, A. M. 31 2014 Analysis of the Gibbs sampler for hierarchical inverse problems. Zbl 1308.62097Agapiou, Sergios; Bardsley, Johnathan M.; Papaspiliopoulos, Omiros; Stuart, Andrew M. 19 2014 Well-posed Bayesian geometric inverse problems arising in subsurface flow. Zbl 1304.35767Iglesias, Marco A.; Lin, Kui; Stuart, Andrew M. 18 2014 Analysis of the 3DVAR filter for the partially observed Lorenz ’63 model. Zbl 1283.62194Law, Kody; Shukla, Abhishek; Stuart, Andrew 14 2014 Bayesian posterior contraction rates for linear severely ill-posed inverse problems. Zbl 1288.62036Agapiou, Sergios; Stuart, Andrew M.; Zhang, Yuan-Xiang 13 2014 Noisy gradient flow from a random walk in Hilbert space. Zbl 1308.60005Pillai, Natesh S.; Stuart, Andrew M.; Thiéry, Alexandre H. 6 2014 Determining white noise forcing from Eulerian observations in the Navier-Stokes equation. Zbl 1310.60095Hoang, Viet Ha; Law, Kody J. H.; Stuart, Andrew M. 4 2014 MCMC methods for functions: modifying old algorithms to make them faster. Zbl 1331.62132Cotter, S. L.; Roberts, G. O.; Stuart, A. M.; White, D. 143 2013 Ensemble Kalman methods for inverse problems. Zbl 1311.65064Iglesias, Marco A.; Law, Kody J. H.; Stuart, Andrew M. 64 2013 MAP estimators and their consistency in Bayesian nonparametric inverse problems. Zbl 1281.62089Dashti, M.; Law, K. J. H.; Stuart, A. M.; Voss, J. 56 2013 Optimal tuning of the hybrid Monte Carlo algorithm. Zbl 1287.60090Beskos, Alexandros; Pillai, Natesh; Roberts, Gareth; Sanz-Serna, Jesus-Maria; Stuart, Andrew 52 2013 Complexity analysis of accelerated MCMC methods for Bayesian inversion. Zbl 1288.65004Hoang, Viet Ha; Schwab, Christoph; Stuart, Andrew M. 36 2013 Posterior contraction rates for the Bayesian approach to linear ill-posed inverse problems. Zbl 1284.62289Agapiou, Sergios; Larsson, Stig; Stuart, Andrew M. 35 2013 Accuracy and stability of the continuous-time 3DVAR filter for the Navier-Stokes equation. Zbl 1271.34013Blömker, D.; Law, K.; Stuart, A. M.; Zygalakis, K. C. 25 2013 Evaluation of Gaussian approximations for data assimilation in reservoir models. Zbl 1393.86020Iglesias, Marco A.; Law, Kody J. H.; Stuart, Andrew M. 22 2013 Posterior consistency via precision operators for Bayesian nonparametric drift estimation in SDEs. Zbl 1256.62047Pokern, Y.; Stuart, A. M.; van Zanten, J. H. 12 2013 Accuracy and stability of filters for dissipative PDEs. Zbl 1350.65102Brett, C. E. A.; Lam, K. F.; Law, K. J. H.; McCormick, D. S.; Scott, M. R.; Stuart, A. M. 11 2013 Sparse deterministic approximation of Bayesian inverse problems. Zbl 1236.62014Schwab, C.; Stuart, A. M. 40 2012 Diffusion limits of the random walk Metropolis algorithm in high dimensions. Zbl 1254.60081Mattingly, Jonathan C.; Pillai, Natesh S.; Stuart, Andrew M. 40 2012 Besov priors for Bayesian inverse problems. Zbl 1243.62032Dashti, Masoumeh; Harris, Stephen; Stuart, Andrew 31 2012 Optimal scaling and diffusion limits for the Langevin algorithm in high dimensions. Zbl 1272.60053Pillai, Natesh S.; Stuart, Andrew M.; Thiéry, Alexandre H. 31 2012 Nonparametric estimation of diffusions: a differential equations approach. Zbl 1437.62575Papaspiliopoulos, Omiros; Pokern, Yvo; Roberts, Gareth O.; Stuart, Andrew M. 18 2012 Variational data assimilation using targetted random walks. Zbl 1426.76629Cotter, S. L.; Dashti, M.; Stuart, A. M. 8 2012 Multiscale modelling and inverse problems. Zbl 1245.76107Nolen, James; Pavliotis, Grigorios A.; Stuart, Andrew M. 8 2012 \(\Gamma \)-limit for transition paths of maximal probability. Zbl 1260.82039Pinski, F. J.; Stuart, A. M.; Theil, F. 6 2012 Mathematical and algorithmic aspects of atmosphere-ocean data assimilation. Abstracts from the workshop held December 2–8, 2012. Zbl 1349.00174 1 2012 Parameter estimation for multiscale diffusions: an overview. Zbl 1375.62022Pavliotis, Grigorios A.; Pokern, Yvo; Stuart, Andrew M. 1 2012 Riemann manifold Langevin and Hamiltonian Monte Carlo methods. With discussion and authors’ reply. Zbl 1411.62071Girolami, Mark; Calderhead, Ben 129 2011 Uncertainty quantification and weak approximation of an elliptic inverse problem. Zbl 1234.35309Dashti, M.; Stuart, A. M. 37 2011 Hybrid Monte Carlo on Hilbert spaces. Zbl 1235.60091Beskos, A.; Pinski, F. J.; Sanz-Serna, J. M.; Stuart, A. M. 30 2011 A note on diffusion limits of chaotic skew-product flows. Zbl 1220.37009Melbourne, I.; Stuart, A. M. 28 2011 Signal processing problems on function space: Bayesian formulation, stochastic PDEs and effective MCMC methods. Zbl 1262.94012Hairer, M.; Stuart, A.; Voss, J. 14 2011 Kalman filtering and smoothing for linear wave equations with model error. Zbl 1230.62128Lee, Wonjung; McDougall, D.; Stuart, A. M. 5 2011 Sampling conditioned hypoelliptic diffusions. Zbl 1219.60062Hairer, Martin; Stuart, Andrew M.; Voss, Jochen 5 2011 Inverse problems: a Bayesian perspective. Zbl 1242.65142Stuart, A. M. 395 2010 Convergence of numerical time-averaging and stationary measures via Poisson equations. Zbl 1217.65014Mattingly, Jonathan C.; Stuart, Andrew M.; Tretyakov, M. V. 35 2010 Approximation of Bayesian inverse problems for PDEs. Zbl 1210.35284Cotter, S. L.; Dashti, M.; Stuart, A. M. 32 2010 Random-weight particle filtering of continuous time processes. Zbl 1411.60109Fearnhead, Paul; Papaspiliopoulos, Omiros; Roberts, Gareth O.; Stuart, Andrew 9 2010 Optimal scalings for local Metropolis-Hastings chains on nonproduct targets in high dimensions. Zbl 1172.60328Beskos, Alexandros; Roberts, Gareth; Stuart, Andrew 39 2009 Bayesian inverse problems for functions and applications to fluid mechanics. Zbl 1228.35269Cotter, S. L.; Dashti, M.; Robinson, J. C.; Stuart, A. M. 26 2009 Maximum likelihood drift estimation for multiscale diffusions. Zbl 1171.62047Papavasiliou, A.; Pavliotis, G. A.; Stuart, A. M. 22 2009 Parameter estimation for partially observed hypoelliptic diffusions. Zbl 1231.62152Pokern, Yvo; Stuart, Andrew M.; Wiberg, Petter 20 2009 Sampling conditioned diffusions. Zbl 1203.60100Hairer, Martin; Stuart, Andrew; Voß, Jochen 8 2009 Calculating effective diffusivities in the limit of vanishing molecular diffusion. Zbl 1161.65007Pavliotis, G. A.; Stuart, A. M.; Zygalakis, K. C. 8 2009 Remarks on drift estimation for diffusion processes. Zbl 1183.62145Pokern, Yvo; Stuart, Andrew M.; Vanden-Eijnden, Eric 3 2009 Computational complexity of Metropolis-Hastings methods in high dimensions. Zbl 1184.65002Beskos, Alexandros; Stuart, Andrew 2 2009 Multiscale methods. Averaging and homogenization. Zbl 1160.35006Pavliotis, Grigorios A.; Stuart, Andrew M. 240 2008 MCMC methods for diffusion bridges. Zbl 1159.65007Beskos, Alexandros; Roberts, Gareth; Stuart, Andrew; Voss, Jochen 52 2008 A first course in continuum mechanics. Zbl 1143.74001Gonzalez, Oscar; Stuart, Andrew M. 29 2008 Data assimilation: mathematical and statistical perspectives. Zbl 1384.62300Apte, A.; Jones, C. K. R. T.; Stuart, A. M.; Voss, J. 13 2008 MCMC methods for sampling function space. Zbl 1179.65003Beskos, Alexandros; Stuart, Andrew 12 2008 Infinite dimensional random dynamical systems and their applications. Abstracts from the workshop held November 2nd – November 8th, 2008. Zbl 1177.37006 2 2008 Analysis of SPDEs arising in path sampling. II: The nonlinear case. Zbl 1140.60329Hairer, M.; Stuart, A. M.; Voss, J. 41 2007 ...and 77 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 3,841 Authors 86 Stuart, Andrew M. 30 Mao, Xuerong 29 Kloeden, Peter Eris 21 Pavliotis, Grigorios A. 20 Yuan, Chenggui 19 Law, Kody J. H. 19 Titi, Edriss Saleh 18 Marzouk, Youssef M. 17 Beskos, Alexandros 17 Gan, Siqing 17 Girolami, Mark A. 17 Jasra, Ajay 17 Schwab, Christoph 17 Stoltz, Gabriel 16 Hairer, Martin 15 Danca, Marius-Florin 15 Gander, Martin Jakob 15 Higham, Desmond J. 15 Huang, Chengming 15 Jentzen, Arnulf 15 Roberts, Gareth O. 13 Chaplain, Mark A. J. 13 Reich, Sebastian 13 Shen, Jie 13 Spiliopoulos, Konstantinos V. 13 Wen, Liping 12 Colli, Pierluigi 12 Sanz-Alonso, Daniel 12 Sanz-Serna, Jesús María 12 Tong, Xin Thomson 12 Wang, Xiaojie 12 Wehr, Jan 11 Byrne, Helen Mary 11 Ghattas, Omar N. 11 Gil, Antonio J. 11 Kevrekidis, Ioannis George 11 Kim, Junseok 11 Li, Jinglai 11 Majda, Andrew J. 11 Robinson, James Cooper 11 Trillos, Nicolás García 11 Wu, Fuke 11 Xiao, Aiguo 10 Abdulle, Assyr 10 Cui, Tiangang 10 Ding, Xiaohua 10 Gottwald, Georg A. 10 Hosseini, Bamdad 10 Iglesias, Marco A. 10 Latz, Jonas 10 Lee, Hyun Geun 10 Ottobre, Michela 10 Pillai, Natesh S. 10 Schütte, Christof 10 Shin, Jaemin 10 Tempone, Raúl F. 10 Vanden-Eijnden, Eric 10 Wu, Shulin 9 Bou-Rabee, Nawaf M. 9 Chen, Peng 9 Gilardi, Gianni 9 Harlim, John 9 Lelièvre, Tony 9 Lubuma, Jean Mbaro-Saman 9 Ortigosa, Rogelio 9 Teel, Andrew Richard 9 Tian, Hongjiong 9 Ullmann, Elisabeth 9 Wang, Wansheng 9 Zong, Xiaofeng 8 Alexanderian, Alen 8 Bréhier, Charles-Edouard 8 Dunlop, Matthew M. 8 Garay, Barnabas M. 8 Hutzenthaler, Martin 8 Jiang, Lijian 8 Jiang, Yaolin 8 Liu, Mingzhu 8 Moulines, Eric 8 Nešić, Dragan 8 Nickl, Richard 8 Norbury, John W. 8 Oates, Chris J. 8 Owhadi, Houman 8 Papaioannou, Iason 8 Roberts, Anthony John 8 Roininen, Lassi 8 Sprekels, Jürgen 8 Teckentrup, Aretha L. 8 Wang, Xiaoming 8 Weber, Hendrik 7 Bao, Jianhai 7 Bardsley, Johnathan M. 7 Betsch, Peter 7 Bonfoh, Ahmed S. 7 Buckwar, Evelyn 7 Burger, Martin 7 Calvetti, Daniela 7 Crisan, Dan O. 7 Del Moral, Pierre ...and 3,741 more Authors all top 5 Cited in 373 Serials 149 Journal of Computational Physics 144 Journal of Computational and Applied Mathematics 92 SIAM/ASA Journal on Uncertainty Quantification 81 SIAM Journal on Scientific Computing 63 Computer Methods in Applied Mechanics and Engineering 61 Applied Mathematics and Computation 58 Inverse Problems 58 Applied Numerical Mathematics 49 Statistics and Computing 48 Journal of Statistical Physics 47 Journal of Mathematical Analysis and Applications 46 Computers & Mathematics with Applications 46 Physica D 37 SIAM Journal on Numerical Analysis 35 The Annals of Applied Probability 35 Multiscale Modeling & Simulation 34 Stochastic Processes and their Applications 31 Journal of Scientific Computing 30 BIT 29 Journal of Difference Equations and Applications 28 Mathematics of Computation 28 Numerische Mathematik 27 International Journal of Computer Mathematics 24 Journal of Differential Equations 23 Computational Geosciences 23 SIAM Journal on Applied Dynamical Systems 23 Communications in Computational Physics 20 Numerical Algorithms 20 Bernoulli 20 Communications in Nonlinear Science and Numerical Simulation 19 Journal of Nonlinear Science 18 Chaos 18 Discrete and Continuous Dynamical Systems. 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