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Inference Methods for Models With Noisy and Expensive Likelihoods;
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sampling; Studies in Applied Mathematics; Vol. 148; No. 3;
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Bayesian Inversion Using Multiscale Dynamics; SIAM Journal on
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learning-based multiscale method and its application to inelastic impact
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analysis of weighted Laplacians arising in data clustering; Applied
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consistency of semi-supervised regression on graphs; Inverse
Problems; Vol. 37; No. 10; Art. No. 105011; 10.1088/1361-6420/ac1e80
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Random Feature Model for Input-Output Maps between Banach Spaces;
SIAM Journal on Scientific Computing; Vol. 43; No. 5; A3212-A3243; 10.1137/20M133957X
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and Uncertainty Quantification of Convective Parameters in an Idealized
GCM; Journal of Advances in Modelling Earth Systems; Vol. 13; No. 9;
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Analog Forecasting: Multiscale Test Problems; Multiscale Modeling
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of empirical Bayes and kernel flow for hierarchical parameter
estimation; Mathematics of Computation; Vol. 90; 2527-2578; 10.1090/mcom/3649
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emulate, sample; Journal of Computational Physics; Vol. 424; Art.
No. 109716; 10.1016/j.jcp.2020.109716
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Time Analysis of Momentum Methods; Journal of Machine Learning
Research; Vol. 22; No. 17; 1-40
- Abdulle, Assyr; Garegnani, Giacomo; et el. (2020) Drift
Estimation of Multiscale Diffusions Based on Filtered Data;
Foundations of Computational Mathematics; 10.1007/s10208-021-09541-9
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Data and Zero Noise Limits of Graph-Based Semi-Supervised Learning
Algorithms; Applied and Computational Harmonic Analysis; Vol. 49;
No. 2; 655-697; 10.1016/j.acha.2019.03.005
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Bayesian and Perimeter Regularization for Binary Inversion; SIAM
Journal on Scientific Computing; Vol. 42; No. 4; A1984-A2013; 10.1137/18M1179559
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of Semi-Supervised Learning Algorithms on Graphs: Probit and One-Hot
Methods; Journal of Machine Learning Research; Vol. 21; 1-55; 10.48550/arXiv.1906.07658
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Characterization at Downhole Arrays by Joint Inversion of Dispersion
Data and Acceleration Time Series; Bulletin of the Seismological
Society of America; Vol. 110; No. 3; 1323-1337; 10.1785/0120190256
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optical tomography in the Bayesian framework; Multiscale Modeling
and Simulation; Vol. 18; No. 2; 589-611; 10.1137/19M1247346
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Regularization Within Ensemble Kalman Inversion; SIAM Journal on
Numerical Analysis; Vol. 58; No. 2; 1263-1294; 10.1137/19M1242331
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optimal transport; SIAM Journal on Applied Mathematics; Vol. 80;
No. 1; 599-619; 10.1137/19M1261122
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Langevin Diffusions: Gradient Structure and Ensemble Kalman Sampler;
SIAM Journal on Applied Dynamical Systems; Vol. 19; No. 1; 412-441; 10.1137/19M1251655
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convergence rates of probabilistic integrators for ordinary differential
equations; Statistics and Computing; Vol. 29; No. 6; 1265-1283; 10.1007/s11222-019-09898-6
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Limit For The Random Walk Metropolis Algorithm Out Of stationarity;
Annales De l’Institut Henri Poincaré - Probabilitiés et Statistiques;
Vol. 55; No. 3; 1599-1648; 10.1214/18-AIHP929
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Kalman Inversion: A Derivative-Free Technique For Machine Learning
Tasks; Inverse Problems; Vol. 35; No. 9; Art. No. 095005; 10.1088/1361-6420/ab1c3a
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Kalman Methods With Constraints; Inverse Problems; Vol. 35; No. 9;
Art. No. 095007; PMCID PMC7677878; 10.1088/1361-6420/ab1c09
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and Accuracy of Optimal Particle Filters for Bayesian Data
Assimilation; Chinese Annals of Mathematics, Series B; Vol. 40;
No. 5; 811-842; 10.1007/s11401-019-0161-5
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estimation for macroscopic pedestrian dynamics models from microscopic
data; SIAM Journal on Applied Mathematics; Vol. 79; No. 4;
1475-1500; 10.1137/18M1215980
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quantification for semi-supervised multi-class classification in image
processing and ego-motion analysis of body-worn videos; Electronic
Imaging; Vol. 2019; Art. No. 264; 10.2352/ISSN.2470-1173.2019.11.IPAS-264
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machine learning: how data assimilation leverages physiologic knowledge
using Bayesian inference to forecast the future, infer the present, and
phenotype; Journal of the American Medical Informatics Association;
Vol. 25; No. 10; 1392-1401; PMCID PMC6188514; 10.1093/jamia/ocy106
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Deep Are Deep Gaussian Processes?; Journal of Machine Learning
Research; Vol. 19; No. 54; 1-46; 10.48550/arXiv.1711.11280
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phase of the MALA algorithm; Stochastics and Partial Differential
Equations: Analysis and Computations; Vol. 6; No. 3; 446-499; PMCID
PMC6411168; 10.1007/s40072-018-0113-1
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for ensemble Kalman inversion; Inverse Problems; Vol. 34; No. 5;
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Quantification in Graph-Based Classification of High Dimensional
Data; SIAM/ASA Journal on Uncertainty Quantification; Vol. 6; No. 2;
568-595; 10.1137/17M1134214
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error estimates for trajectories of SPDEs for Spectral Galerkin
discretization; Journal of Computational Mathematics; Vol. 36;
No. 2; 159-182; 10.4208/jcm.1607-m2016-0539
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consistency for Gaussian process approximations of Bayesian posterior
distributions; Mathematics of Computation; Vol. 87; No. 310;
721-753; 10.1090/mcom/3244
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Updating of Model Error for Bayesian Inversion; Inverse Problems;
Vol. 34; No. 2; Art. No. 025008; 10.1088/1361-6420/aaa34d
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analysis of ensemble Kalman inversion: the linear, noisy case;
Applicable Analysis: An International Journal; Vol. 97; No. 1; 107-123;
10.1080/00036811.2017.1386784
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System Modeling 2.0: A Blueprint for Models That Learn From Observations
and Targeted High-Resolution Simulations; Geophysical Research
Letters; Vol. 44; No. 24; 12396-12417; 10.1002/2017GL076101
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Approximations for Probability Measures on R^d; SIAM/ASA Journal on
Uncertainty Quantification; Vol. 5; No. 1; 1136-1165; 10.1137/16M1105384
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Bayesian level set inversion; Statistics and Computing; Vol. 27;
No. 6; 1555-1584; 10.1007/s11222-016-9704-8
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Approximations of Small Noise Diffusions in Kullback-Leibler
Divergence; Communications in Mathematical Sciences; Vol. 15; No. 7;
2087-2097; 10.4310/CMS.2017.v15.n7.a13
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Sampling: Intrinsic Dimension and Computational Cost; Statistical
Science; Vol. 32; No. 3; 405-431; 10.1214/17-STS611
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Approximations for Transition Paths in Brownian Dynamics; SIAM
Journal on Mathematical Analysis; Vol. 49; No. 4; 3005-3047; 10.1137/16M1071845
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analysis of differential equations: introducing probability measures on
numerical solutions; Statistics and Computing; Vol. 27; No. 4;
1065-1082; 10.1007/s11222-016-9671-0
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of the ensemble Kalman filter for inverse problems; SIAM Journal on
Numerical Analysis; Vol. 55; No. 3; 1264-1290; 10.1137/16M105959X
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Carlo and Multilevel Monte Carlo Methods for Computing Posterior
Expectations in Elliptic Inverse Problems; SIAM/ASA Journal on
Uncertainty Quantification; Vol. 5; No. 1; 493-518; 10.1137/16M1061692
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MCMC for Infinite-Dimensional Inverse Problems; Journal of
Computational Physics; Vol. 335; 327-351; 10.1016/j.jcp.2016.12.041
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and analysis of simplified filters; Communications in Mathematical
Sciences; Vol. 15; No. 2; 413-450; 10.4310/CMS.2017.v15.n2.a6
- Iglesias, Marco A.; Lin, Kui; et el. (2017) Filter
Based Methods For Statistical Linear Inverse Problems;
Communications in Mathematical Sciences; Vol. 15; No. 7; 1867-1896; 10.4310/CMS.2017.v15.n7.a4
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Bayesian formulation of EIT: Analysis and algorithms; Inverse
Problems and Imaging; Vol. 10; No. 4; 1007-1036; 10.3934/ipi.2016030
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estimators for piecewise continuous inversion; Inverse Problems;
Vol. 32; No. 10; Art. No. 105003; 10.1088/0266-5611/32/10/105003
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accuracy for the Lorenz 96 model: fixed versus adaptive observation
operators; Physica D: Nonlinear Phenomena; Vol. 325; 1-13; 10.1016/j.physd.2015.12.008
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Statistics and Data Science; EMS Newsletter; Vol. 100; 28-30
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Function Space HMC Algorithm With Second Order Langevin Diffusion
Limit; Bernoulli; Vol. 22; No. 1; 60-106; 10.3150/14-BEJ621
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Bayesian Level Set Method for Geometric Inverse Problems; Interfaces
and Free Boundaries; Vol. 18; No. 2; 181-217; 10.4171/IFB/362
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Asymptotics of the Filtering Distribution for Partially Observed Chaotic
Dynamical Systems; SIAM/ASA Journal on Uncertainty Quantification;
Vol. 3; No. 1; 1200-1220; 10.1137/140997336
- Beskos, Alexandros; Jasra, Ajay; et el. (2015) Sequential
Monte Carlo methods for Bayesian elliptic inverse problems;
Statistics and Computing; Vol. 25; No. 4; 727-737; 10.1007/s11222-015-9556-7
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Multiscale Analysis of Diffusions on Rapidly Varying Surfaces;
Journal of Nonlinear Science; Vol. 25; No. 2; 389-449; 10.1007/s00332-015-9237-x
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for Kullback–Leibler Approximation of Probability Measures in Infinite
Dimensions; SIAM Journal on Scientific Computing; Vol. 37; No. 6;
A2733-A2757; 10.1137/14098171X
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Assimilation: New Challenges in Random and Stochastic Dynamical
Systems; SIAM News; Vol. 48; No. 8 & 9
- Pinski, F. J.; Simpson, G.; et el. (2015) Kullback-Leibler
approximation for probability measures on infinite dimensional
spaces; SIAM Journal on Mathematical Analysis; Vol. 47; No. 6;
4091-4122; 10.1137/140962802
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gaps for a Metropolis–Hastings algorithm in infinite dimensions;
Annals of Applied Probability; Vol. 24; No. 6; 2455-2490; 10.1214/13-AAP982
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Bayesian geometric inverse problems arising in subsurface flow;
Inverse Problems; Vol. 30; No. 11; Art. No. 114001; 10.1088/0266-5611/30/11/114001
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and accuracy of the ensemble Kalman filter in discrete and continuous
time; Nonlinearity; Vol. 27; No. 10; 2579-2603; 10.1088/0951-7715/27/10/2579
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of the Gibbs Sampler for Hierarchical Inverse Problems; SIAM/ASA
Journal on Uncertainty Quantification; Vol. 2; No. 1; 511-544; 10.1137/130944229
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posterior contraction rates for linear severely ill-posed inverse
problems; Journal of Inverse and Ill-posed Problems; Vol. 22; No. 3;
297-321; 10.1515/jip-2012-0071
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white noise forcing from Eulerian observations in the Navier-Stokes
equation; Stochastic Partial Differential Equations: Analysis and
Computations; Vol. 2; No. 2; 233-261; 10.1007/s40072-014-0028-4
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gradient flow from a random walk in Hilbert space; Stochastic
Partial Differential Equations: Analysis and Computations; Vol. 2;
No. 2; 196-232; 10.1007/s40072-014-0029-3
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of the 3DVAR filter for the partially observed Lorenz’63 model;
Discrete and Continuous Dynamical Systems A; Vol. 34; No. 3; 1061-1078;
10.3934/dcds.2014.34.1061
- Iglesias, Marco and Stuart, Andrew M. (2014) Inverse
Problems and Uncertainty Quantification; SIAM News; 2-3
- Beskos, Alexandros; Pillai, Natesh; et el. (2013) Optimal
tuning of the hybrid Monte Carlo algorithm; Bernoulli; Vol. 19;
No. 5A; 1501-1534; 10.3150/12-BEJ414
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contraction rates for the Bayesian approach to linear ill-posed inverse
problems; Stochastic Processes and their Applications; Vol. 123;
No. 10; 3828-3860; 10.1016/j.spa.2013.05.001
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estimators and their consistency in Bayesian nonparametric inverse
problems; Inverse Problems; Vol. 29; No. 9; Art. No. 095017; 10.1088/0266-5611/29/9/095017
- Cotter, S. L.; Roberts, G. O.; et el. (2013) MCMC
Methods for Functions: Modifying Old Algorithms to Make Them Faster;
Statistical Science; Vol. 28; No. 3; 424-446; 10.1214/13-STS421
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analysis of accelerated MCMC methods for Bayesian inversion; Inverse
Problems; Vol. 29; No. 8; Art No. 085010; 10.1088/0266-5611/29/8/085010
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and stability of the continuous-time 3DVAR filter for the Navier–Stokes
equation; Nonlinearity; Vol. 26; No. 8; 2193-2219; 10.1088/0951-7715/26/8/2193
- Iglesias, Marco A.; Law, Kody; et el. (2013) Evaluation
of Gaussian approximations for data assimilation in reservoir
models; Computational Geosciences; Vol. 17; No. 5; 851-885; 10.1007/s10596-013-9359-x
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Kalman methods for inverse problems; Inverse Problems; Vol. 29;
No. 4; Art. No. 045001; 10.1088/0266-5611/29/4/045001
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and stability of filters for dissipative PDEs; Physica D: Nonlinear
Phenomena; Vol. 245; No. 1; 34-35; 10.1016/j.physd.2012.11.005
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consistency via precision operators for Bayesian nonparametric drift
estimation in SDEs; Stochastic Processes and their Applications;
Vol. 123; No. 2; 603-628; 10.1016/j.spa.2012.08.010
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scaling and diffusion limits for the Langevin algorithm in high
dimensions; Annals of Applied Probability; Vol. 22; No. 6;
2320-2356; 10.1214/11-AAP828
- Law, K. J. H. and Stuart, A. M. (2012) Evaluating
Data Assimilation Algorithms; Monthly Weather Review; Vol. 140;
3757-3782; 10.1175/MWR-D-11-00257.1
- Papaspiliopoulos, Omiros; Pokern, Yvo; et el. (2012) Nonparametric
estimation of diffusions: a differential equations approach;
Biometrika; Vol. 99; No. 3; 511-531; 10.1093/biomet/ass034
- Mattingly, Jonathan C.; Pillai, Natesh S.; et el. (2012) Diffusion
limits of the random walk Metropolis algorithm in high dimensions;
Annals of Applied Probability; Vol. 22; No. 3; 881-930; 10.1214/10-AAP754
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priors for Bayesian inverse problems; Inverse Problems and Imaging;
Vol. 6; No. 2; 183-200; 10.3934/ipi.2012.6.183
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determinisitc approximation of Bayesian inverse problems; Inverse
Problems; Vol. 28; No. 4; Art. No. 045003; 10.1088/0266-5611/28/4/045003
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for Transition Paths of Maximal Probability; Journal of Statistical
Physics; Vol. 146; No. 5; 955-974; 10.1007/s10955-012-0443-8
- Cotter, S. L.; Dashti, M.; et el. (2012) Variational
data assimilation using targetted random walks; International
Journal for Numerical Methods in Fluids; Vol. 68; No. 4; 403-421; 10.1002/fld.2510
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Quantification and Weak Approximation of an Elliptic Inverse
Problem; SIAM Journal on Numerical Analysis; Vol. 49; No. 6;
2524-2542; 10.1137/100814664
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Monte Carlo on Hilbert spaces; Stochastic Processes and their
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filtering and smoothing for linear wave equations with model error;
Inverse Problems; Vol. 27; No. 9; Art. No. 095008; 10.1088/0266-5611/27/9/095008
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note on diffusion limits of chaotic skew-product flows;
Nonlinearity; Vol. 24; No. 4; 1361-1367; 10.1088/0951-7715/24/4/018
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conditioned hypoelliptic diffusions; Annals of Applied Probability;
Vol. 21; No. 2; 669-698; 10.1214/10-AAP708
- Fearnhead, Paul; Papaspiliopoulos, Omiros; et el. (2010) Random-weight
particle filtering of continuous time processes; Journal of the
Royal Statistical Society: Series B; Vol. 72; No. 4; 497-512; 10.1111/j.1467-9868.2010.00744.x
- Fearnhead, Paul; Papaspiliopoulos, Omiros; et el. (2010) Random-weight
particle filtering of continuous time processes; Statistical
Methodology; Vol. 72; No. 4; 497-512; 10.1111/j.1467-9868.2010.00744.x
- Pinski, F. J. and Stuart, A. M. (2010) Transition
paths in molecules at finite temperature; Journal of Chemical
Physics; Vol. 132; No. 18; Art. No. 184104; 10.1063/1.3391160
- Mattingly, J. C.; Stuart, A. M.; et el. (2010) Convergence
of numerical time-averaging and stationary measures via Poisson
equations; SIAM Journal of Numerical Analysis; Vol. 48; No. 2;
552-577; 10.1137/090770527
- Stuart, A. M. (2010) Inverse
problems: A Bayesian perspective; Acta Numerica; Vol. 19; 451-559;
10.1017/S0962492910000061
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of Bayesian Inverse Problems for PDEs; SIAM Journal on Numerical
Analysis; Vol. 48; No. 1; 322-345; 10.1137/090770734
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inverse problems for functions and applications to fluid mechanics;
Inverse Problems; Vol. 25; No. 11; Art. No 115008; 10.1088/0266-5611/25/11/115008
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on Drift Estimation for Diffusion Processes; Multiscale Modeling and
Simulation; Vol. 8; No. 1; 69-95; 10.1137/070694806
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likelihood drift estimation for multiscale diffusions; Stochastic
Processes and their Applications; Vol. 119; No. 10; 3173-3210; 10.1016/j.spa.2009.05.003
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scalings for local Metropolis–Hastings chains on nonproduct targets in
high dimensions; Annals of Applied Probability; Vol. 19; No. 3;
863-898; 10.1214/08-AAP563
- Pavliotis, G. A.; Stuart, A. M.; et el. (2009) Calculating
effective diffusivities in the limit of vanishing molecular
diffusion; Journal of Computational Physics; Vol. 288; No. 4;
1030-1055; 10.1016/j.jcp.2008.10.014
- Pokern, Yvo; Stuart, Andrew M.; et el. (2009) Parameter
estimation for partially observed hypo-elliptic diffusions; Journal
of the Royal Society: Series B (Statistical Methodology); Vol. 71;
No. 1; 49-73; 10.1111/j.1467-9868.2008.00689.x
- Pokern, Yvo; Stuart, Andrew M.; et el. (2009) Parameter
estimation for partially observed hypoelliptic diffusions;
Statistical Methodology; Vol. 71; No. 1; 49-73; 10.1111/j.1467-9868.2008.00689.x
- Beskos, Alexandros; Roberts, Gareth; et el. (2008) MCMC
Methods for Diffusion Bridges; Stochastics and Dynamics; Vol. 8;
No. 3; 319-350; 10.1142/S0219493708002378
- Apte, A.; Jones, C. K. R. T.; et el. (2008) Data
assimilation: Mathematical and statistical perspectives;
International Journal for Numerical Methods in Fluids; Vol. 56; No. 8;
1033-1046; 10.1002/fld.1698
- Apte, A.; Jones, C. K. R. T.; et el. (2008) A
Bayesian approach to Lagrangian data assimilation; Tellus A; Vol.
60; No. 2; 336-347; 10.1111/j.1600-0870.2007.00295.x
- Lamba, H.; Mattingly, J. C.; et el. (2007) An
adaptive Euler-Maruyama scheme for SDEs: convergence and stability;
IMA Journal of Numerical Analysis; Vol. 27; No. 3; 479-506; 10.1093/imanum/drl032
- Apte, A.; Hairer, M.; et el. (2007) Sampling
the posterior: An approach to non-Gaussian data assimilation;
Physica D; Vol. 230; No. 1-2; 50-64; 10.1016/j.physd.2006.06.009
- Pavliotis, G. A. and Stuart, A. M. (2007) Parameter
Estimation for Multiscale Diffusions; Journal of Statistical
Physics; Vol. 127; No. 4; 741-781; 10.1007/s10955-007-9300-6
- Hairer, M.; Stuart, A. M.; et el. (2007) Analysis
of SPDEs arising in path sampling part II: The nonlinear case;
Annals of Applied Probability; Vol. 17; No. 5/6; 1657-1706; 10.1214/07-AAP441
- Pavliotis, G. A.; Stuart, A. M.; et el. (2007) Homogenization
for inertial particles in a random flow; Communications in
Mathematical Sciences; Vol. 5; No. 3; 507-531; 10.4310/CMS.2007.v5.n3.a1
- Barkley, D.; Kevrekidis, I. G.; et el. (2006) The
Moment Map: Nonlinear Dynamics of Density Evolution via a Few
Moments; SIAM Journal on Applied Dynamical Systems; Vol. 5; No. 3;
403-434; 10.1137/050638667
- Pavliotis, G. A. and Stuart, A. M. (2005) Analysis
of White Noise Limits for Stochastic Systems with Two Fast Relaxation
Times; Multiscale Modeling and Simulation; Vol. 4; No. 1; 1-35; 10.1137/040610507
- Pavliotis, G. A. and Stuart, A. M. (2005) Periodic
homogenization for inertial particles; Physica D; Vol. 204; No. 3-4;
161-187; 10.1016/j.physd.2005.04.011
- Hairer, M.; Stuart, A. M.; et el. (2005) Analysis
of SPDEs arising in path sampling. Part I: The Gaussian case;
Communications in Mathematical Sciences; Vol. 3; No. 4; 587-603; 10.4310/CMS.2005.v3.n4.a8
- Kupferman, R. and Stuart, A. M. (2004) Fitting
SDE models to nonlinear Kac–Zwanzig heat bath models; Physica D;
Vol. 199; No. 3-4; 279-316; 10.1016/j.physd.2004.04.011
- Stuart, Andrew M.; Voss, Jochen; et el. (2004) Conditional
Path Sampling of SDEs and the Langevin MCMC Method; Communications
in Mathematical Sciences; Vol. 2; No. 4; 685-697; 10.4310/CMS.2004.v2.n4.a7
- Givon, Dror; Kupferman, Raz; et el. (2004) Extracting
macroscopic dynamics: model problems and algorithms; Nonlinearity;
Vol. 17; No. 6; R55-R127; 10.1088/0951-7715/17/6/R01
- Kupferman, R.; Pavliotis, G. A.; et el. (2004) Itô
versus Stratonovich white-noise limits for systems with inertia and
colored multiplicative noise; Physical Review E; Vol. 70; No. 3;
Art. No. 036120; 10.1103/PhysRevE.70.036120
- Pavliotis, G. A. and Stuart, A. M. (2003) White
Noise Limits for Inertial Particles in a Random Field; Multiscale
Modeling and Simulation; Vol. 1; No. 4; 527-553; 10.1137/S1540345903421076
- Huisinga, Wilhelm; Schütte, Christof; et el. (2003) Extracting
macroscopic stochastic dynamics: Model problems; Communications on
Pure and Applied Mathematics; Vol. 56; No. 2; 234-269; 10.1002/cpa.10057
- Higham, Desmond J.; Mao, Xuerong; et el. (2003) Exponential
Mean-Square Stability of Numerical Solutions to Stochastic Differential
Equations; LMS Journal of Computation and Mathematics; Vol. 6;
297-313; 10.1112/S1461157000000462
- Kupferman, R.; Stuart, A. M.; et el. (2002) Long-Term
Behavior of Large Mechanical Systems with Random Initial Data;
Stochastics and Dynamics; Vol. 02; No. 04; 533-562; 10.1142/S0219493702000571
- Sigurgeirsson, H. and Stuart, A. M. (2002) A
model for preferential concentration; Physics of Fluids; Vol. 14;
No. 12; 4352-4361; 10.1063/1.1517603
- Mattingly, J. C.; Stuart, A. M.; et el. (2002) Ergodicity
for SDEs and approximations: locally Lipschitz vector fields and
degenerate noise; Stochastic Processes and their Applications; Vol.
101; No. 2; 185-232; 10.1016/S0304-4149(02)00150-3
- Higham, Desmond J.; Mao, Xuerong; et el. (2002) Strong
Convergence of Euler-Type Methods for Nonlinear Stochastic Differential
Equations; SIAM Journal on Numerical Analysis; Vol. 40; No. 3;
1041-1063; 10.1137/S0036142901389530
- Estep, Donald J. and Stuart, Andrew M. (2002) The
dynamical behavior of the discontinuous Galerkin method and related
difference schemes; Mathematics of Computation; Vol. 71; No. 239;
1075-1103; 10.1090/S0025-5718-01-01364-3
- Sigurgeirsson, H. and Stuart, A. M. (2002) Inertial
Particles in a Random Field; Stochastics and Dynamics; Vol. 02;
No. 02; 295-310; 10.1142/S021949370200042X
- Mattingly, J. C. and Stuart, A. M. (2002) Geometric
Ergodicity of Some Hypo-Elliptic Diffusions for Particle Motions;
Markov Processes And Related Fields; Vol. 8; No. 2; 199-214
- Sigurgeirsson, Hersir; Stuart, Andrew; et el. (2001) Algorithms
for Particle-Field Simulations with Collisions; Journal of
Computational Physics; Vol. 172; No. 2; 766-807; 10.1006/jcph.2001.6858
- Cano, B. and Stuart, A. M. (2001) Underresolved
Simulations of Heat Baths; Journal of Computational Physics; Vol.
169; No. 1; 193-214; 10.1006/jcph.2001.6722
- Cano, B.; Stuart, A. M.; et el. (2001) Stiff
Oscillatory Systems, Delta Jumps and White Noise; Foundations of
Computational Mathematics; Vol. 1; No. 1; 69-100; 10.1007/s10208001002
- Shardlow, T. and Stuart, A. M. (2000) A
Perturbation Theory for Ergodic Markov Chains and Application to
Numerical Approximations; SIAM Journal on Numerical Analysis; Vol.
37; No. 4; 1120-1137; 10.1137/S0036142998337235
- Stuart, A. M. and Warren, J. O. (1999) Analysis
and Experiments for a Computational Model of a Heat Bath; Journal of
Statistical Physics; Vol. 97; No. 3/4; 687-723; 10.1023/A:1004667325896
- Sanz-Serna, J. M. and Stuart, A. M. (1999) Ergodicity
of Dissipative Differential Equations Subject to Random Impulses;
Journal of Differential Equations; Vol. 155; No. 2; 262-284; 10.1006/jdeq.1998.3594
- Gonzalez, O.; Higham, D. J.; et el. (1999) Qualitative
properties of modified equations; IMA Journal of Numerical Analysis;
Vol. 19; No. 2; 169-190; 10.1093/imanum/19.2.169
- Lamba, H. and Stuart, A. M. (1998) Convergence
results for the MATLAB ODE23 routine; BIT Numerical Mathematics;
Vol. 38; No. 4; 751-780; 10.1007/BF02510413
- Gander, Martin J. and Stuart, Andrew M. (1998) Space-Time
Continuous Analysis of Waveform Relaxation for the Heat Equation;
SIAM Journal on Scientific Computing; Vol. 19; No. 6; 2014-2031; 10.1137/S1064827596305337
- Budd, C. J.; Koomullil, G. P.; et el. (1998) On
the Solution of Convection-Diffusion Boundary Value Problems Using
Equidistributed Grids; SIAM Journal on Scientific Computing; Vol.
20; No. 2; 591-618; 10.1137/S1064827595280454
- Jones, Don A.; Stuart, Andrew M.; et el. (1998) Persistence
of Invariant Sets for Dissipative Evolution Equations; Journal of
Mathematical Analysis and Applictions; Vol. 219; No. 2; 479-502; 10.1006/jmaa.1997.5847
- Higham, D. J. and Stuart, A. M. (1998) Analysis
of the dynamics of local error control via a piecewise continuous
residual; BIT Numerical Mathematics; Vol. 38; No. 1; 44-57; 10.1007/BF02510916
- Bjørhus, Morten and Stuart, Andrew M. (1997) Waveform
relaxation as a dynamical system; Mathematics of Computation; Vol.
66; No. 219; 1101-1118; 10.1090/S0025-5718-97-00847-8
- Stuart, A. M. (1997) Probabilistic
and deterministic convergence proofs for software for initial value
problems; Numerical Algorithms; Vol. 14; No. 1/3; 227-260; 10.1023/A:1019169114976
- Elliott, C. M. and Stuart, A. M. (1996) Viscous
Cahn–Hilliard Equation II. Analysis; Journal of Differential
Equations; Vol. 128; No. 2; 387-414; 10.1006/jdeq.1996.0101
- Jones, D. A. and Stuart, A. M. (1995) Attractive
Invariant Manifolds under Approximation. Inertial Manifolds; Journal
of Differential Equations; Vol. 123; No. 2; 588-637; 10.1006/jdeq.1995.1174
- Stuart, A. M. and Humphries, A. R. (1995) The
Essential Stability of Local Error Control for Dynamical Systems;
SIAM Journal on Numerical Analysis; Vol. 32; No. 6; 1940-1971; 10.1137/0732087
- Estep, Donald J. and Stuart, Andrew M. (1995) The
rate of error growth in Hamiltonian-conserving integrators;
Zeitschrift für Angewandte Mathematik und Physik; Vol. 46; No. 3;
407-418; 10.1007/BF01003559
- Lord, Gabriel J. and Stuart, Andrew M. (1995) Discrete
Gevrey regularity attractors and uppers–semicontinuity for a finite
difference approximation to the Ginzburg–Landau equation; Numerical
Functional Analysis and Optimization; Vol. 16; No. 7-8; 1003-1047; 10.1080/01630569508816658
- Bai, F.; Elliott, C. M.; et el. (1995) The
viscous Cahn-Hilliard equation. I. Computations; Nonlinearity; Vol.
8; No. 2; 131-160; 10.1088/0951-7715/8/2/002
- Bai, Fengshan; Spence, Alastair; et el. (1994) Numerical
computations of coarsening in the one-dimensional Cahn-Hilliard model of
phase separation; Physica D; Vol. 78; No. 3-4; 155-165; 10.1016/0167-2789(94)90112-0
- Humphries, A. R. and Stuart, A. M. (1994) Runge–Kutta
Methods for Dissipative and Gradient Dynamical Systems; SIAM Journal
on Numerical Analysis; Vol. 31; No. 5; 1452-1485; 10.1137/0731075
- Budd, C. J.; Dold, J. W.; et el. (1994) Blow-up
in a System of Partial Differential Equations with Conserved First
Integral. Part II: Problems with Convection; SIAM Journal on Applied
Mathematics; Vol. 54; No. 3; 610-640; 10.1137/S0036139992232131
- Stuart, A. M. and Humphries, A. R. (1994) Model
Problems in Numerical Stability Theory for Initial Value Problems;
SIAM Review; Vol. 36; No. 2; 226-257; 10.1137/1036054
- Stuart, Andrew M. (1994) Numerical
analysis of dynamical systems; Acta Numerica; Vol. 3; 467-572; 10.1017/S0962492900002488
- Elliott, C. M. and Stuart, A. M. (1993) The
Global Dynamics of Discrete Semilinear Parabolic Equations; SIAM
Journal on Numerical Analysis; Vol. 30; No. 6; 1622-1663; 10.1137/0730084
- Chaplain, M. A. J. and Stuart, A. M. (1993) A
model mechanism for the chemotactic response of endothelial cells to
tumour angiogenesis factor; Mathematical Medicine and Biology; Vol.
10; No. 3; 149-168; 10.1093/imammb/10.3.149
- Budd, Chris; Dold, Bill; et el. (1993) Blowup
in a Partial Differential Equation with Conserved First Integral;
SIAM Journal on Applied Mathematics; Vol. 53; No. 3; 718-742; 10.1137/0153036
- Bai, Fengshan; Spence, Alastair; et el. (1993) The
Numerical Computation of Heteroclinic Connections in Systems of Gradient
Partial Differential Equations; SIAM Journal on Applied Mathematics;
Vol. 53; No. 3; 743-769; 10.1137/0153037
- Iserles, A. and Stuart, A. M. (1992) Unified
approach to spurious solutions introduced by time discretization Part
II: BDF-like methods; IMA Journal of Numerical Analysis; Vol. 12;
No. 4; 487-502; 10.1093/imanum/12.4.487
- Griffiths, D. F.; Stuart, A. M.; et el. (1992) Numerical
Wave Propagation in an Advection Equation with a Nonlinear Source
Term; SIAM Journal on Numerical Analysis; Vol. 29; No. 5; 1244-1260;
10.1137/0729074
- Sanz-Serna, J. M. and Stuart, A. M. (1992) A
note on uniform in time error estimates for approximations to
reaction-diffusion equations; IMA Journal of Numerical Analysis;
Vol. 12; No. 3; 457-462; 10.1093/imanum/12.3.457
- Iserles, A.; Peplow, A. T.; et el. (1991) A
Unified Approach to Spurious Solutions Introduced by Time
Discretisation. Part I: Basic Theory; SIAM Journal on Numerical
Analysis; Vol. 28; No. 6; 1723-1751; 10.1137/0728086
- Stuart, A. M. and Peplow, A. T. (1991) The
Dynamics of the Theta Method; SIAM Journal on Scientific and
Statistical Computing; Vol. 12; No. 6; 1351-1372; 10.1137/0912074
- Chaplain, M. A. J. and Stuart, A. M. (1991) A
Mathematical Model for the Diffusion of Tumour Angiogenesis Factor into
the Surrounding Host Tissue; Mathematical Medicine and Biology; Vol.
8; No. 3; 191-220; 10.1093/imammb/8.3.191
- Stuart, Andrew M. (1991) Singular
Limits in Free Boundary Problems; Rocky Mountain Journal of
Mathematics; Vol. 21; No. 2; 809-811; 10.1216/rmjm/1181072969
- Stuart, A. M. and Floater, M. S. (1990) On
the computation of blow-up; European Journal of Applied Mathematics;
Vol. 1; No. 01; 47-71; 10.1017/S095679250000005X
- Stuart, Andrew (1989) Linear
Instability Implies Spurious Periodic Solutions; IMA Journal of
Numerical Analysis; Vol. 9; No. 4; 465-486; 10.1093/imanum/9.4.465
- Stuart, Andrew (1989) Nonlinear
Instability in Dissipative Finite Difference Schemes; SIAM Review;
Vol. 31; No. 2; 191-220; 10.1137/1031048
- Norbury, J. and Stuart, A. M. (1989) A
Model for Porous-Medium Combustion; Quarterly Journal of Mechanics
and Applied Mathematics; Vol. 42; No. 1; 159-178; 10.1093/qjmam/42.1.159
- Stuart, A. M. (1989) Singular
Free Boundary Problems and Local Bifurcation Theory; SIAM Journal on
Applied Mathematics; Vol. 49; No. 1; 72-85; 10.1137/0149004
- Stuart, Andrew (1989) A
Note on High/Low-Wave-Number Interactions in Spatially Discrete
Parabolic Equations; IMA Journal of Applied Mathematics; Vol. 42;
No. 1; 27-42; 10.1093/imamat/42.1.27
- Stuart, Andrew (1988) Similarity
Solutions of a Heat Equation with Nonlinearly Varying Heat Capacity;
IMA Journal of Applied Mathematics; Vol. 40; No. 3; 217-234; 10.1093/imamat/40.3.217
- Norbury, J. and Stuart, A. M. (1988) Travelling
Combustion Waves in a Porous Medium. Part II—Stability; SIAM Journal
on Applied Mathematics; Vol. 48; No. 2; 374-392; 10.1137/0148019
- Norbury, J. and Stuart, A. M. (1988) Travelling
Combustion Waves in a Porous Medium. Part I—Existence; SIAM Journal
on Applied Mathematics; Vol. 48; No. 1; 155-169; 10.1137/0148007
- Norbury, J. and Stuart, A. M. (1987) Parabolic
Free Boundary Problems Arising in Porous Medium Combustion; IMA
Journal of Applied Mathematics; Vol. 39; No. 3; 241-257; 10.1093/imamat/39.3.241
- Stuart, A. M. (1987) Existence
of Solutions of a Two-Point Free-Boundary Problem Arising in the Theory
of Porous Medium Combustion; IMA Journal of Applied Mathematics;
Vol. 38; No. 1; 23-34; 10.1093/imamat/38.1.23
- Norbury, J. and Stuart, A. M. (1987) Volterra
integral equations and a new Gronwall inequality (Part I: The linear
case); Proceedings of the Royal Society of Edinburgh: Section A
Mathematics; Vol. 106; No. 3-4; 361-373; 10.1017/S0308210500018473
- Norbury, J. and Stuart, A. M. (1987) Volterra
integral equations and a new Gronwall inequality (Part II: The nonlinear
case); Proceedings of the Royal Society of Edinburgh: Section A
Mathematics; Vol. 106; No. 3-4; 375-384; 10.1017/S0308210500018485