The first talk is given by Prof. Dan Crisan (Imperial College London) on Particle Approximations For Partially Observed Fluid Dynamics Models.
Abstract
Fluid dynamics models are ubiquitous in a multitude of applications. One of the most important applications of fluid dynamics models is numerical weather prediction. Modern numerical weather prediction combines sophisticated nonlinear fluid dynamics models with increasingly accurate high-dimensional data. This process is called data assimilation and it is performed every day at all major operational weather centers across the world. Data assimilation (DA) requires massive computing capabilities as realistic atmosphere-ocean models typically have billions of degrees of freedom. I will give a short overview of the ongoing research that aims to drastically decrease the required DA computational effort by reducing the dimension of the models involved and using stochastic perturbations to account for the unresolved scales. The incorporation of observation data is done by using particle approximations suitably adapted to solve high-dimensional problems.
The second talk is given by Prof. Alexandros Beskos (University College London) on Manifold Markov Chain Monte Carlo Methods for Bayesian Inference In Diffusion Models.
Abstract
Bayesian inference for nonlinear diffusions, observed at discrete times,is a challenging task that has prompted the development of a number of algorithms, mainly within the computational statistics community. We propose a new direction, and accompanying methodology - borrowing ideas from statistical physics and computational chemistry - for inferring the posterior distribution of latent diffusion paths and model parameters, given observations of the process. Joint configurations of the underlying process noise and of parameters, mapping onto diffusion paths consistent with observations, form an implicitly defined manifold. Then, by making use of a constrained Hamiltonian Monte Carlo algorithm on the embedded manifold, we are able to perform computationally efficient inference for a class of discretely observed diffusion models. Critically, in contrast with other approaches proposed in the literature, our methodology is highly automated, requiring minimal user intervention and applying alike in a range of settings, including: elliptic or hypo-elliptic systems; observations with or without noise; linear or non-linear observation operators. Exploiting Markovianity, we propose a variant of the method with complexity that scales linearly in the resolution of path discretisation and the number of observation times. Example Python code is given at git.io/m-mcmc.