[00410] Recent advances in Bayesian optimal experimental design
Session Time & Room : 2D (Aug.22, 15:30-17:10) @G304
Type : Proposal of Minisymposium
Abstract : Computational measurement models may involve several uncertain parameters in addition to the unknown quantities of primary interest. In Bayesian optimal experimental design, the goal is to design a measurement configuration, e.g. optimal placement of sensors to collect observational data, which maximizes the expected utility---such as the expected information gain---for obtaining information on the unknown quantities subject to uncertainties in the measurement model. This is especially important when there is a limited budget for collecting actual measurement data. This minisymposium showcases recent theoretical and computational developments to overcome the major challenges encountered in problems arising within this field.
[04376] A transport map approach for Bayesian optimal experimental design
Format : Talk at Waseda University
Author(s) :
Karina Koval (Heidelberg University)
Roland Herzog (Heidelberg University)
Robert Scheichl (Heidelberg University)
Abstract : Solving the Bayesian optimal experimental design (BOED) problem requires optimizing an expectation of a utility function or optimality criterion that assesses the quality of each design. For Bayesian inverse problems with non-Gaussian posteriors, a closed-form expression for the criterion is typically unavailable. Thus, access to a computationally efficient approximation is crucial for numerical solution of the optimal design problem. We propose a flexible approach for approximating the expected utility function and solving the BOED problem that is based on transportation of measures. The key to our method is the approximation of the joint density on the design, observation and inference parameter random variables via the pushforward of a simple reference density under an inverse Knothe-Rosenblatt (KR) rearrangement. This KR map exposes certain conditional densities which enables approximation of the optimality criterion for any design choice. We present our approach and assess the effectiveness of the resulting optimal designs with some numerical examples.
[04957] Accelerating A-Optimal Design of Experiments Using Neural Networks
Format : Talk at Waseda University
Author(s) :
Jinwoo Go (Georgia Institute of Technology)
Peng Chen (Georgia Institute of Technology)
Abstract : Designing experiments for large-scale problems demands significant computational resources, and Partial Differential Equation (PDE) surrogates have emerged as a widely-adopted approach to address this challenge. This study enhances this methodology by independently training PDE surrogates and their Jacobians. Leveraging the trained Jacobian of PDEs, we approximate the posterior covariance matrix. Subsequently, we compute the trace of this matrix and evaluate the reduction in uncertainty resulting from executing the experimental setup.
[05059] Stability of Bayesian optimal experimental design in inverse problem
Format : Talk at Waseda University
Author(s) :
Tapio Helin (LUT University)
Jose Rodrigo Rojo Garcia (LUT University)
Duc-Lam Duong (LUT University)
Abstract : In this talk, I will explore the stability properties of Bayesian optimal experimental design towards misspecification of distributions or numerical approximations. Specifically, I will present a framework for addressing this problem in a non-parametric setting, and demonstrate a stability result for the expected utility with respect to likelihood perturbations. To provide a more concrete illustration, I will then consider non-linear Bayesian inverse problems with Gaussian likelihood, where the forward mapping is replaced by an approximation.
[05080] Quasi-Monte Carlo methods for Design of Experiment
Format : Talk at Waseda University
Author(s) :
Claudia Schillings (FU Berlin)
Vesa Kaarnioja (Free University of BerlinFU Berlin)
Abstract : Bayesian experimental design aims to optimize the placement of measurements in an experiment such that information about unknown quantities is maximized (w.r. to a suitable criterion). The optimization problem requires the evaluation of the information gain, which corresponds to the evaluation of an integral w.r. to the posterior distribution. We will explore the use of quasi-Monte Carlo methods for Bayesian design problems in this talk and present convergence results.
