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Uncertainty Quantification and Inverse Problems

Levi, Finland, 24–28 March 2024

This event will bring together experts working on various aspects of data assimilation, uncertainty quantification, and inverse problems.


The event will be held on 24–28 March 2024 and it consists of a series of talks in three thematic subcategories: Data Assimilation, Space Physics, and Uncertainty Quantification and Partial Differential Equations


This event is organized by Vesa Kaarnioja, Jana de Wiljes, and Lassi Roininen. Contact person: vesa.kaarnioja@fu-berlin.de


  • Iris Rammelmüller (Universität Klagenfurt)
    Title: Stepwise data absorption combining complementary filtering techniques

    Abstract: Data Assimilation serves multiple purposes, including estimating the model state and the initial state of a system for predicting its future state. It combines prior information from numerical model simulations with observed data to produce the most accurate description of a dynamical system and its uncertainty. Here we introduce additional importance sampling steps by splitting the likelihood in order to improve the robustness and accuracy of the estimations. This approach allows us to combine Gaussian approximative filters such as the Ensemble Square Root Filter (ESRF) and consistent filters such as the Ensemble Transform Particle Filter (ETPF). The benefit is that one can exploit the stabilizing properties of ESRF type filters while mimicking the accuracy level of a consistent filter.
  • Jana de Wiljes (TU Ilmenau)
    Title: Projection induced localization for ensemble data-assimilation methods

    Abstract: There is a high demand to predict and understand systems where information is available in the form of observations and models, such as those based on first principles. Bayesian sequential learning methods are among the most advanced techniques that can be used in this context. However, the large spatial scale and complexity of these systems still pose significant computational challenges. To address this, many techniques make simplifying assumptions, such as assuming a Gaussian distribution, which can lead to less accurate predictions. However, less restrictive (in the distributional sense) filters tend to suffer more heavily from the curse of dimensionality than their Gaussian approximative filter counterparts. To combat this problem, several numerical improvement tools have been developed over the last two decades. One of the most popular techniques is localization, which leverages the fact that short-range spatial interactions are a key feature of dynamics in many applications. In this context, we introduce an enhanced localisation technique that utilizes prior projection of the state. Consistent filters such as sequential Monte Carlo particularly benefit from this type of localisation.
  • Alejandra Avalos Pacheco (TU Wien)

    Title: Efficient Bayesian integrative factor models: Applications from nutritional epidemiology to cancer genomics

    Abstract: Data integration of multiple studies can be key to understanding and gaining knowledge in statistical research. Such complex data present artifactual sources of variation, also known as covariate effects, that, if not corrected, could lead to unreliable inference. Traditional multi-study factor analysis (MSFA) have proven to be key for identifying reproducible signal of interest shared by different studies or populations, which traditional factor analysis may miss. Bayesian inference for such models relies on Markov Chain Monte Carlo (MCMC) methods, which scale poorly. Furthermore, MSFA does not include relevant covariates in the model that could bias the results. Both problems are tackled by (i) introducing variational inference algorithms to approximate the posterior distribution of Sparse MSFA, and (ii) presenting novel multi-study factor regression (MSFR) models to jointly learn common and study-specific factors while adjusting for covariate effects. The usefulness of the methods is shown in nutritional epidemiology and cancer genomic applications to (i) obtain dietary patterns, and their association with cardiometabolic disease risk for Hispanic groups and (ii) reveal biological pathways for ovarian cancer datasets using computational resources typically available on a laptop rather than a high-performance computing server.

  • Lassi Roininen (LUT University)

    Title: Detecting rough features with non-Gaussian models

    Abstract: We consider recent advances in using non-Gaussian and hierarchical mixture models for estimating rough features, such as edges, material interfaces, and similar, in Bayesian inverse problems. We go through the recent developments, and papers associated, and also future research directions.

  • Emma Hannula (LUT University)

    Title: Time series prediction with Bayesian Neural Networks

  • Angelina Senchukova (LUT University)
    Title: Edge-preserving priors based on Gaussian scale mixtures for Bayesian inverse problems

    Abstract: In large-scale inverse problems like image deblurring and X-ray computed tomography, preserving sharp features in the solution is crucial. Within the Bayesian framework for inverse problems, this task can be achieved using Markov random field priors that follow heavy-tailed probability distributions. In this study, we introduce a family of edge-preserving priors that combines the structure of first-order Markov random fields with Student's t distribution. To enhance the efficiency of posterior sampling, we exploit the Gaussian scale mixture representation of this heavy-tailed distribution, employing a hierarchical Gibbs sampler. We demonstrate the performance of the prior on linear Bayesian inverse problems.