Problems at the Applied Mathematics / Statistics Interface
Lead Research Organisation:
University of Warwick
Department Name: Mathematics
Abstract
Mathematics is the language of science, and applied mathematics is concerned with developing models with predictive capability, and with probing those models to obtain qualitative and quantitative insight into the phenomena being modelled. Statistics is data-driven and is aimed at the development of methodologies to optimize the information derived from data. The increasing complexity of phenomena that scientists and engineers wish to model, together with our increased ability to gather, store and interrogate data, mean that the subjects of applied mathematics and statistics are increasingly required to work in conjunction in order to significantly progress understanding.The research will facilitate the development of research at the interface between applied mathematics and statistics, both by the study of fundamental theoretical questions, and by their application to problems of importance in science and technology, such as chemical reactions and weather prediction.The work will thus make fundamental progress on theoretical research questions in mathematics and statistics, and will have direct application in a range of applications from the physical sciences and beyond.
Organisations
People |
ORCID iD |
| Andrew Stuart (Principal Investigator) |
Publications
Agapiou S
(2013)
Posterior contraction rates for the Bayesian approach to linear ill-posed inverse problems
in Stochastic Processes and their Applications
Beskos A
(2013)
Optimal tuning of the hybrid Monte Carlo algorithm
in Bernoulli
Beskos A
(2011)
Hybrid Monte Carlo on Hilbert spaces
in Stochastic Processes and their Applications
Blömker D
(2013)
Accuracy and stability of the continuous-time 3DVAR filter for the Navier-Stokes equation
in Nonlinearity
Brett C
(2013)
Accuracy and stability of filters for dissipative PDEs
in Physica D: Nonlinear Phenomena
Bréhier C
(2018)
Weak Error Estimates for Trajectories of SPDEs Under Spectral Galerkin Discretization
in Journal of Computational Mathematics
Cano B
(2013)
Stiff Oscillatory Systems, Delta Jumps and White Noise
in Foundations of Computational Mathematics
Cotter S
(2013)
MCMC Methods for Functions: Modifying Old Algorithms to Make Them Faster
in Statistical Science
Cotter S
(2010)
Approximation of Bayesian Inverse Problems for PDEs
in SIAM Journal on Numerical Analysis
Cotter S
(2011)
Variational data assimilation using targetted random walks
in International Journal for Numerical Methods in Fluids
Dashti M
(2011)
Uncertainty Quantification and Weak Approximation of an Elliptic Inverse Problem
in SIAM Journal on Numerical Analysis
Dashti M
(2013)
MAP estimators and their consistency in Bayesian nonparametric inverse problems
in Inverse Problems
Fearnhead P
(2010)
Random-Weight Particle Filtering of Continuous Time Processes
in Journal of the Royal Statistical Society Series B: Statistical Methodology
Hairer M
(2011)
Sampling conditioned hypoelliptic diffusions
in The Annals of Applied Probability
Hairer, M., Stuart, A.M. And Voss, J.
(2011)
The Oxford Handbook of Nonlinear Filtering
Hoang V
(2013)
Complexity analysis of accelerated MCMC methods for Bayesian inversion
in Inverse Problems
Iglesias M
(2013)
Evaluation of Gaussian approximations for data assimilation in reservoir models
in Computational Geosciences
Iglesias M
(2013)
Ensemble Kalman methods for inverse problems
in Inverse Problems
Kessler M
(2012)
Statistical Methods for Stochastic Differential Equations
Lee W
(2011)
Kalman filtering and smoothing for linear wave equations with model error
in Inverse Problems
Mattingly J
(2012)
Diffusion limits of the random walk Metropolis algorithm in high dimensions
in The Annals of Applied Probability
Mattingly J
(2010)
Convergence of Numerical Time-Averaging and Stationary Measures via Poisson Equations
in SIAM Journal on Numerical Analysis
Melbourne I
(2011)
A note on diffusion limits of chaotic skew-product flows
in Nonlinearity
Nolen J
(2012)
Numerical Analysis of Multiscale Problems
Papaspiliopoulos O
(2012)
Nonparametric estimation of diffusions: a differential equations approach
in Biometrika
Pillai N
(2012)
Optimal scaling and diffusion limits for the Langevin algorithm in high dimensions
in The Annals of Applied Probability
Pinski F
(2012)
G-Limit for Transition Paths of Maximal Probability
in Journal of Statistical Physics
Pinski F
(2010)
Transition paths in molecules at finite temperature
in The Journal of Chemical Physics
Pokern Y
(2013)
Posterior consistency via precision operators for Bayesian nonparametric drift estimation in SDEs
in Stochastic Processes and their Applications
Schwab C
(2012)
Sparse deterministic approximation of Bayesian inverse problems
in Inverse Problems
Stuart A
(2012)
Evaluating Data Assimilation Algorithms
in Monthly Weather Review
Stuart A
(2012)
Besov priors for Bayesian inverse problems
in Inverse Problems and Imaging
Stuart A
(2010)
Inverse problems: A Bayesian perspective
in Acta Numerica