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The geometry of optimal experiment design for vector-valued Ornstein-Uhlenbeck processes.

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SNA - Theoretical foundations for statistical network analysis

Ornstein-Uhlenbeck processes are commonly used as models in engineering, biology and finance. Consider the estimation of the state of such processes from linear, noisy measurements; the Kalman filter is known to be the minimum mean square error estimator when the measurement noise is Gaussian. We address here how to design the measurements that minimize the error afforded by the Kalman filter. This problem of optimal experiment design, which is almost as old as the Kalman filter itself,  is however not convex. As a consequence, many ad hoc methods have been used over the years to solve it. We show in this talk how a geometric approach allows us to characterize and obtain the optimal designs exactly. This optimal design yields the lowest possible estimation error from linear measurements with a fixed signal to noise ratio. 


This talk is part of the Isaac Newton Institute Seminar Series series.

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BAS Seminar Room 1; https://ukri.zoom.us/j/93328878449 In person in the Max Perutz Lecture Theatre (CB2 0QH) and via Zoom link https://mrc-lmb-cam-ac-uk.zoom.us/j/94132066038?pwd=OF2EjwrvRQxl0XgpGK0N5L4bDNaayi.1 Gordon Cameron Lecture Theatre, Fitzwilliam College, Cambridge

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