On Bayesian A- and D-optimal experimental designs in infinite dimensions

By Alen Alexanderian, P. Gloor, Omar Ghattas. 2014

92 citations recorded by the source corpus.

We consider Bayesian linear inverse problems in infinite-dimensional separable Hilbert spaces, with a Gaussian prior measure and additive Gaussian noise model, and provide an extension of the concept of Bayesian D-optimality to the infinite-dimensional case. To this end, we derive the infinite-dimensional version of the expression for the Kullback-Leibler divergence from the posterior measure to the prior measure, which is subsequently used to derive the expression for the expected information gain. We also study the notion of Bayesian A-optimality in the infinite-dimensional setting, and extend the well known (in the finite-dimensional case) equivalence of the Bayes risk of the MAP estimator with the trace of the posterior covariance, for the Gaussian linear case, to the infinite-dimensional Hilbert space case.

Subfields: Computational Theory and Mathematics, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d3c30e2f9bc67d9d66dbb84b402106f69d3afcaf

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Chris J. Oates
2. T. Sullivan
3. Jon Cockayne
4. Andrew M. Stuart
5. Masoumeh Dashti
6. Mark A. Girolami
7. Paris Perdikaris
8. Yibo Yang

In Management Science and Operations Research

1. Chris J. Oates
2. T. Sullivan
3. Jon Cockayne
4. Andrew M. Stuart
5. Masoumeh Dashti
6. Mark A. Girolami
7. Theodore Papamarkou

In Statistics and Probability

1. Chris J. Oates
2. Mark A. Girolami
3. Jon Cockayne
4. T. Sullivan
5. Masoumeh Dashti
6. Andrew M. Stuart
7. Paris Perdikaris
8. Qiang Liu

Citations in the corpus

• Probabilistic Meshless Methods for Partial Differential Equations and Bayesian Inverse Problems (2016, background): “In particular, the Aoptimality criteria above is equivalent to minimising the trace of the posterior covariance operator ∫ D σ(x)2dx, while D-optimality minimises the volume of the uncertainty ellipsoid [Alexanderian et al., 2016a].”
• The Bayesian Approach to Inverse Problems (2013, methodology): “On the algorithmic side, algorithms for Bayesian inversion in geophysical applications are formulated in [16, 81], and on the computational statistics side, methods for optimal experimental design are formulated in [5, 6].”