Optimálne navrhovanie blokových experimentov
Alena Bachratá
PhD thesis advisor: Radoslav Harman

PhD thesis - Full text    (1059 kB)
Autoreferat    (364 kB)

Optimal design of block experiments The main topic of the dissertation thesis is the optimal design of block experiments. We are looking for such design, that maximizes amount of information for unknown parameters of interest of linear regression model. The optimal design must be from the set of all feasible designs, which are determined by constraints on resources. We work with a big class of optimality criteria - with orthogonally invariant information criteria. We focus on block experiments with the block size two, which can be represented by concurrence graphs. There are two kinds of results. Firstly, we show some theoretically derived classes of Schur-optimal augmentation of designs, found by applying results from graph theory. These classes are the optimal augmentations of designs, which have following concurrence graphs: Star graphs, Complete graphs, and Complete regular multipartite graphs. Secondly, we present three novel stochastic algorithms for finding optimal exact designs with respect to the set of resource constraints. In the end of the thesis, we show numerical results of these algorithms and propose hypotheses based on the results.

Related papers
[1] Harman, R., Bachratá A., Filová L. 2015
Construction of efficient experimental designs under multiple resource constrains Applied Stochastic Models in Business and Industry [elektronický zdroj].

[2] Bachratá, A., Harman, R. 2013
A stochastic optimization method for constructing optimal block designs with linear constraints 18th European Young Statisticians Meeting. - Osijek : J. J. Strossmayer University, 2014. - S. 147-151. - ISBN 978-953-6931-70-5