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  • 2015-2019  (4)
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  • 1
    Publication Date: 2020-08-05
    Description: We consider a stationary discrete-time linear process that can be observed by a finite number of sensors. The experimental design for the observations consists of an allocation of available resources to these sensors. We formalize the problem of selecting a design that maximizes the information matrix of the steady-state of the Kalman filter, with respect to a standard optimality criterion, such as $D-$ or $A-$optimality. This problem generalizes the optimal experimental design problem for a linear regression model with a finite design space and uncorrelated errors. Finally, we show that under natural assumptions, a steady-state optimal design can be computed by semidefinite programming.
    Language: English
    Type: conferenceobject , doc-type:conferenceObject
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  • 2
    Publication Date: 2020-08-05
    Description: We prove a mathematical programming characterisation of approximate partial D-optimality under general linear constraints. We use this characterisation with a branch-and-bound method to compute a list of all exact D-optimal designs for estimating a pair of treatment contrasts in the presence of a nuisance time trend up to the size of 24 consecutive trials.
    Language: English
    Type: conferenceobject , doc-type:conferenceObject
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  • 3
    Publication Date: 2020-08-05
    Description: Let the design of an experiment be represented by an $s-$dimensional vector $w$ of weights with nonnegative components. Let the quality of $w$ for the estimation of the parameters of the statistical model be measured by the criterion of $D-$optimality, defined as the $m$th root of the determinant of the information matrix $M(w)=\sum_{i=1}^s w_i A_i A_i^T$, where $A_i$,$i=1,\ldots,s$ are known matrices with $m$ rows. In this paper, we show that the criterion of $D-$optimality is second-order cone representable. As a result, the method of second-order cone programming can be used to compute an approximate $D-$optimal design with any system of linear constraints on the vector of weights. More importantly, the proposed characterization allows us to compute an exact $D-$optimal design, which is possible thanks to high-quality branch-and-cut solvers specialized to solve mixed integer second-order cone programming problems. Our results extend to the case of the criterion of $D_K-$optimality, which measures the quality of $w$ for the estimation of a linear parameter subsystem defined by a full-rank coefficient matrix $K$. We prove that some other widely used criteria are also second-order cone representable, for instance, the criteria of $A-$, $A_K$-, $G-$ and $I-$optimality. We present several numerical examples demonstrating the efficiency and general applicability of the proposed method. We show that in many cases the mixed integer second-order cone programming approach allows us to find a provably optimal exact design, while the standard heuristics systematically miss the optimum.
    Language: English
    Type: article , doc-type:article
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  • 4
    Publication Date: 2020-08-05
    Description: We prove a mathematical programming characterisation of approximate partial D-optimality under general linear constraints. We use this characterisation with a branch-and-bound method to compute a list of all exact D-optimal designs for estimating a pair of treatment contrasts in the presence of a nuisance time trend up to the size of 24 consecutive trials.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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