Organisers:

• Charles-Edouard Bréhier, CNRS & Université Lyon 1
  
• Evelyn Buckwar, Linz University
  
• Erika Hausenblas, Loeben University
  
• Ray Kawai, Tokyo University
  
• Gabriel Lord, Radboud University
  
• Mikhail Tretyakov, Nottingham University
  
• Kostas Zygalakis, Edinburgh University
  

This is a One World Seminar. The seminars occur bi-weekly on a Wednesday 13.00 - 14.00 BST

Click here to register

Recordings from this seminar series are available here.

 Next Seminar

1 December
Aretha Teckentrup (University of Edinburgh)
Convergence, Robustness and Flexibility of Gaussian Process Regression

We are interested in the task of estimating an unknown function from a set of point evaluations. In this context, Gaussian process regression is often used as a Bayesian inference procedure. However, hyper-parameters appearing in the mean and covariance structure of the Gaussian process prior, such as smoothness of the function and typical length scales, are often unknown and learnt from the data, along with the posterior mean and covariance.

In the first part of the talk, we will study the robustness of Gaussian process regression with respect to mis-specification of the hyper-parameters, and provide a convergence analysis of the method applied to a fixed, unknown function of interest [1].
In the second part of the talk, we discuss deep Gaussian processes as a class of flexible non-stationary prior distributions [2].
[1] A.L. Teckentrup. Convergence of Gaussian process regression with estimated hyper-parameters and applications in Bayesian inverse problems. SIAM/ASA Journal on Uncertainty Quantification, 8(4), p.1310-1337, 2020.
[2] M.M. Dunlop, M.A. Girolami, A.M. Stuart, A.L. Teckentrup. How deep are deep Gaussian processes? Journal of Machine Learning Research, 19(54), 1-46, 2018.

Future Seminars

• 15 December 2021: Toshihiro Yamada (Hitotsubashi University)

Previous Seminars

Monika Eisenmann, Lund University - Sub-linear convergence of stochastic optimization methods in Hilbert space

Konstantinos Dareiotis, University of Leeds - Approximation of stochastic equations with irregular drifts

• This seminar was NOT recorded
  

Andrew Stuart, Caltech - Inverse Problems Without Adjoints


Svetlana Dubinkina, Vrije Universiteit Amsterdam - Shadowing approach to data assimilation

Denis Talay, Inria and Ecole Polytechnique - Probability distributions of first hitting times of solutions to SDEs w.r.t. the Hurst parameter of the driving fractional Brownian noise: A sensitivity analysis

Evelyn Buckwar, Johannes Kepler University - A couple of ideas on splitting methods for SDEs

Andreas Prohl, Tübingen - Numerical methods for stochastic Navier-Stokes equations

Mireille Bossy, INRIA - SDEs with boundaries, modelling particle dynamics in turbulent flow

Raphael Kruse, Halle-Wittenberg - On the BDF2-Maruyama method for stochastic evolution equations

Adrien Laurent, University of Geneva - Order conditions for sampling the invariant measure of ergodic stochastic differential equations in R^d and on manifolds

Chuchu Chen, Chinese Academy of Sciences - Probabilistic superiority of stochastic symplectic methods via large deviations principle

• This seminar was NOT recorded
  

 
Kostas Zygalakis, University of Edinburgh - Explicit stabilised Runge-Kutta methods and their application to Bayesian inverse problems

Xuerong Mao, Strathclyde - The Truncated Euler-Maruyama Method for Stochastic Differential Delay Equations

Charles-Edouard Bréhier, Claude Bernard Lyon - Analysis of splitting schemes for the stochastic Allen-Cahn equation

 
Conall Kelly, University College Cork - A hybrid, adaptive numerical method for the Cox-Ingersoll-Ross model

 
Abdul Lateef Haji-Ali, Heriot Watt University - Sub-sampling and other considerations for efficient risk estimation in large portfolios

David Cohen, Umeå University - Drift-preserving schemes for stochastic Hamiltonian and Poisson systems

Gabriel Lord, Radboud University - Numerics and SDE a model for the stochastically forced vorticity equation

Marco Iglesias, University of Nottingham - Ensemble Kalman Inversion: from subsurface environments to composite materials

Ray Kawai, University of Tokyo - Stochastic approximation in adaptive Monte Carlo variance reduction

• This seminar was NOT recorded
  

 
Kody Law, University of Manchester - Bayesian Static Parameter Estimation using Multilevel and multi-index Monte Carlo

Akash Sharma & Michael Tretyakov, University of Nottingham - Computing ergodic limits of reflected diffusions and sampling from distributions with compact support

Georg Gottwald, The University of Sydney - Simulation of non-Lipschitz stochastic differential equations driven by α-stable noise: a method based on deterministic homogenisation

Marta Sanz-Sole, Barcelona - Global existence for stochastic waves with super-linear coefficients

Sonja Cox, University of Amsterdam - Efficient simulation of generalized Whittle-Mat'ern fields

Raul Tempone, KAUST, Combining Hierarchical Approximation with Importance Sampling: Approximation and Optimization techniques

Tony Shardlow, University of Bath, Contaminant dispersal, numerical simulation, and stochastic PDEs

Emmanuel Gobet (Ecole Polytechnique) - How to generate the path of Fractional Brownian motion with a ReLU-Neural Networks


Arturo Kohatsu-Higa (Ritsumeikan University): Simulation of Reflected Brownian motion on two dimensional wedges

• This seminar was NOT recorded 

Irene Tubikanec (Johannes Kepler University, Linz) - plitting methods for SDEs with locally Lipschitz drift. An illustration on the FitzHugh-Nagumo model

• Recording will be available soon
  

Zoom is the online platform being used to deliver this seminar series. If you have any question please contact liam.holligan@icms.org.uk

This seminar series is supported as part of the ICMS Online Mathematical Sciences Seminars.