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barycentric algorithm for computing D-optimal size- and cost-constrained designs of experiments

METRIKA 2017年第2期80卷 201-225页

作者： Harman, Radoslav Benkova, Eva Comenius Univ Fac Math Phys & Informat Bratislava 84248 Slovakia

In this paper, we study the problem of D-optimal experimental design under two linear constraints, which can be interpreted as simultaneous restrictions on the size and on the cost of the experiment. For computing a size- and cost-constrained approximate D-optimal design, we propose a specification of the "barycentric" multiplicative algorithm with sequential removal of redundant design points. We analytically prove convergence results for the proposed algorithm and numerically demonstrate its favorable properties compared to competing methods.

关键词： Optimal design of experiments D-optimality Cost constraints barycentric algorithm

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Multiplicative methods for computing D-optimal stratified designs of experiments

引用

JOURNAL OF STATISTICAL PLANNING AND INFERENCE 2014年 146卷 82-94页

作者： Harman, Radoslav Comenius Univ Dept Appl Math & Stat Fac Math Phys & Informat Bratislava 84248 Slovakia

Consider a linear regression experiment with uncorrelated real-valued observations and a finite design space. An approximate experimental design is stratified if it allocates given proportions of trials to selected non-overlapping partitions of the design space. To calculate an approximate D-optimal stratified design, we propose two multiplicative methods: a re-normalisation heuristic and a barycentric algorithm, both of which are very simple to implement. The re-normalisation heuristic is generally more rapid, but for the barycentric algorithm, we can prove monotonic convergence to the optimum. We also develop rules for the removal of design points that cannot support any D-optimal stratified design, which significantly improves the speed of both proposed multiplicative methods. (C) 2013 Elsevier B.V. All rights reserved.

关键词： D-optimal design Stratified design Marginal constraints Multiplicative algorithm barycentric algorithm

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