BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Talks.cam//talks.cam.ac.uk// X-WR-CALNAME:Talks.cam BEGIN:VEVENT SUMMARY:Sequential Bayesian Inference in high-dimensional geoscience appli cations - Peter Jan van Leeuwen (University of Reading) DTSTART:20180109T143000Z DTEND:20180109T153000Z UID:TALK97483@talks.cam.ac.uk CONTACT:INI IT DESCRIPTION:Applications of sequential Bayesian Inference in the geo sciences\, such as atmosphere\, ocean\, atmospheric chemistry\, and
la nd-surface\, are characterised by high dimensions\, nonlinearity\, and com plex relations between system variables.
While Gaussian-based approxi mations such as Ensemble Kalman Filters and Smoothers and global variation al
methods have been used quite extensively in this field\, numerous p roblems ask for methods that can handle
strong nonlinearities. In this talk I will discuss recent progress using particle filters.

Thre e main areas of active research in particle filtering can be distinguished \, exploring localisation\,
exploring proposal densities\, and explor ing (optimal) transportation (and mergers of these ideas are on the
ho rizon). In localisation the idea is to split the high-dimensional problem in several smaller problems
that then need to be stitched together in a smart way. The first approximate applications of this methodology
h ave just made it to weather prediction\, showing the exponentially fast de velopments here. However\,
the &lsquo\;stitching&rsquo\; problem remai ns outstanding. The proposal density methodology discussed next might be fruitful to incorporate here.

In the proposal density approach one tries to evolve states in state space such that they obtain very simi lar weights
in the particle filter. Challenges are\, of course\, the h uge dimensions\, but these also provide opportunities via
the existenc e of typical sets\, which lead to preferred parts of state space for the p articles. Recent attempts to exploit
typical sets will be discussed.
Finally\, we will discuss recent progress in (optimal) transportat ion. The idea here is that a set of prior particles
has to be transfor med to a set of posterior particles. This is an old problem in optimal tra nsportation. However\,
the optimality condition poses unnecessary cons traints\, and by relaxing the optimality constraint we are able to
fo rmulate new efficient methods. Specifically\, by iteratively minimising th e relative entropy between the probability
density of the prior parti cles and the posterior a sequence of transformations emerges for each part icle that seems
to be tractable even for very high dimensional spaces. A new idea is to explore localisation to obtain a more
accurate descr iption of the target posterior\, but without the stitching issues mentione d above.

So far\, model reduction techniques\, emulation\, and ma chine learning techniques have been unsuccessful for
these high-dimens ional state estimation problems\, but I&rsquo\;m keen to further understan d the possibilities and limitations. LOCATION:Seminar Room 1\, Newton Institute END:VEVENT END:VCALENDAR