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Tytuł artykułu

Adaptive control for sequential design

Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The optimal experiment for estimating the parameters of a nonlinear regression model usually depends on the value of these parameters, hence the problem of designing experiments that are robust with respect to parameter uncertainty. Sequential designpermits to adapt the experiment to the value of the parameters, and can thus be considered as a robust design procedure. By designing theexperiments sequentially, one introduces a feedback of information, and thus dynamics, into the design procedure. Several sequential schemes, corresponding to different control policies, are considered. The optimal one corresponds to closed-loop control, and is solution of a stochastic dynamic-programming problem, which is extremely difficult to solve. A suboptimal strategy is proposed, which relies ona normal approximation of the future posterior of θ, independent of future observations. The design criterion obtained involves several mathematical expectations, which are approximated by Laplace method. Finally, stochastic approximation algorithms are also suggested to determine (sub)optimal sequential experiments without having to compute expectations.
Twórcy
  • CNRS/Université de Nice Sophia Antipolis, France
autor
  • CNRS/Université de Nice Sophia Antipolis, France
Bibliografia
  • [1] R. Bellman, Dynamic Programming, Princeton University Press, Princeton, N. J., 1957.
  • [2] K. Chaloner and I. Verdinelli, Bayesian experimental design: a review, Statistical Science 10 (3) (1995), 273-304.
  • [3] R. Gautier and L. Pronzato, Sequential design and active control, NewDevelopments and Applications in Experimental Design (N. Flournoy, W. F. Rosenberger and W. K. Wong, eds.), IMS Lecture Notes 34 (1998), 138-151.
  • [4] C. Kulcsár, L. Pronzato and E. Walter, Optimal experimental design and therapeutic drug monitoring, Int. Journal of Biomedical Computing 36 (1994), 95-101.
  • [5] C. Kulcsár, L. Pronzato and E. Walter, Dual control of linearly parameterized models via prediction of posterior densities, European J. of Control 2 (1996), 135-143.
  • [6] H. Kushner and G. Yin, Stochastic Approximation Algorithms and Applications, Springer, Heidelberg 1997.
  • [7] J. Pilz, Bayesian Estimation and Experimental Design in Linear Regression Models, vol. 55 Teubner-Texte zur Mathematik, Leipzig, 1983 (also Wiley, New York 1991).
  • [8] L. Pronzato, C. Kulcsár and E. Walter, An actively adaptive control policy for linear models, IEEE Trans. Autom. Cont. 41 (1996), 855-858.
  • [9] L. Pronzato and E. Walter, Robust experiment design via stochastic approximation, Mathematical Biosciences 75 (1985), 103-120.
  • [10] L. Pronzato, E. Walter and C. Kulcsár, A dynamical-system approach to sequential design, Model-Oriented Data Analysis III, Proceedings MODA3, St Petersburg, May 1992 (W. G. Müller, H. P. Wynn and A. A. Zhigljavsky, eds.), Physica Verlag, Heidelberg, 11-24.
  • [11] W. J. Runggaldier, Concepts of optimality in stochastic control, Reliability and Decision (R. Barlow, et al., ed.), Elsevier, Amsterdam, 101-114.
  • [12] M. Tanner, Tools for Statistical Inference Methods for Exploration of Posterior Distributions and Likelihood Functions, Springer, Heidelberg 1993.
  • [13] L. Tierney and J. Kadane, Accurate approximations for posterior moments and marginal densities, Journal of the American Statistical Association 81 (393) (1986), 82-86.
  • [14] S. Zacks, Problems and approaches in design of experiments for estimation and testing in nonlinear models, Multivariate Analysis IV, (P. Krishnaiah, ed.), North Holland, Amsterdam 1977, 209-223.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1006
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