Sensor Clusterization in D-optimal Design in Infinite Dimensional Bayesian Inverse Problems
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We investigate the problem of sensor clusterization in optimal experimental design for infinite-dimensional Bayesian inverse problems. We suggest an analytically tractable model for such designs and reason how it may lead to sensor clusterization in the case of iid measurement noise. We also show that in the case of spatially correlated measurement error clusterization does not occur. As a part of the analysis we prove a matrix determinant lemma analog in infinite dimensions, as well as a lemma for calculating derivatives of log of operators.
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