Mini Seminar Series on „Non-Gaussian large scale Bayesian inversion“

25.11.2020, 12:00-13:30
SFB-Seminar

jointly organised by Jana de Wiljes and the Lappeenranta-Lahti University of Technology (LUT, Finland)

Mini Seminar Series Schedule

12:00-12:30 Jarkko Suuronen (LUT) - tba

12:30-13:00 Sahani Pathiraja (UP) - McKean-Vlasov SDEs in Nonlinear Filtering 

13:00-13:30 Teemu Härkönen (LUT) - tba

Please find abstracts below.

***Due to the current pandemic this event will be conducted online. We invite you to join and spread the news. Please register in order to receive the zoom link for the event by sending  an email up front to Jana de Wiljes<wiljes[at]uni-potsdam.de> ***

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12:00-12:30 Jarkko Suuronen (LUT)

Non-Gaussian random field priors and their MCMC samplers

I will talk about non-Gaussian random field priors in inverse problems from numerical perspective. I briefly demonstrate the advantages and problems of such priors when doing inference with them. For sampling the posteriors with random fields priors, I introduce a few recently proposed MCMC methods that should perform better than the existing widely used methods. Finally, I talk about future directions for research.

12:30-13:00 Sahani Pathiraja (UP)

McKean-Vlasov SDEs in Nonlinear Filtering

A number of particle filters have been proposed over the last couple of decades with the common feature that the update step is governed by a type of control law. This feature makes them an attractive alternative to traditional sequential Monte Carlo which scales poorly with the state dimension due to weight degeneracy. I will discuss a unifying framework that allows to systematically derive the McKean-Vlasov representations of these filters for the discrete time and continuous time observation case, taking inspiration from the smooth approximation of the data considered in earlier work of Crisan and Xiong. Three filters that have been proposed in the literature will be discussed and the framework will be used to derive Ito representations of their limiting forms as the time discretisation parameter goes to zero, as well as their well-posedness.  Connections of these approaches to Bayesian inverse problems will be made in the spirit of the recent work on ensemble Kalman inversion.

13:00-13:30 Teemu Härkönen (LUT)

Efficient multi-scale Gaussian process regression for remote sensing and sequential Monte Carlo mixtures of Gaussian process experts

We have designed and implemented a computationally efficient multi-scale Gaussian process (GP) software package, satGP, geared towards remote sensing applications. The software is able to handle problems of enormous sizes and to compute marginals and sample from the random field conditioning on at least hundreds of millions of observations. This is achieved by optimizing the computation by, e.g., randomization and splitting the problem into parallel local subproblems which aggressively discard uninformative data. Mixtures of Gaussian process experts are capable of of modelling non-stationarities in data. We are developing methods for parallel inference of such models extending previosuly existing methods.