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3-dimensional multivertex reconstruction from 2-dimensional tracks observations using likelihood inference

Nikolai I. Chernov, Genadij A. Ososkov, Luc Pronzato (1992)

Applications of Mathematics

Let v 1 , v 2 , . . . , v k be vertices in the X Y Z -space, each vertex producing several tracks (straight lines) emanating from it within a narrow cone with a small angle about a fixed direction ( Z -axis). Each track is detected (by drift chambers or other detectors) by its projections on X Y and Y Z views independently with small errors. An automated method is suggested for the reconstruction of vertices from noisy observations of the tracks projections. The procedure is based on the likelihood inference for mixtures. An illustrative...

Adaptive biased-coin designs for clinical trials with several treatments

Anthony C. Atkinson (2004)

Discussiones Mathematicae Probability and Statistics

Adaptive designs are used in phase III clinical trials for skewing the allocation pattern towards the better treatments. We use optimum design theory to provide a skewed biased-coin procedure for sequential designs with continuous responses. The skewed designs are used to provide adaptive designs, the performance of which is studied numerically for designs with three treatments. Important properties are loss and the proportion of allocation to inferior treatments. Regularisation to provide consistent...

Adaptive control for sequential design

Roland Gautier, Luc Pronzato (2000)

Discussiones Mathematicae Probability and Statistics

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....

A-optimal biased spring balance weighing design

Małgorzata Graczyk (2011)


In this paper we study the problem of estimation of individual measurements of objects in a biased spring balance weighing design under assumption that the errors are uncorrelated and they have different variances. The lower bound for the variance of each of the estimated measurements for this design and the necessary and sufficient conditions for this lower bound to be attained are given. The incidence matrices of the balanced incomplete block designs are used for construction of the A-optimal...

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