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PhD thesis - Full text (1059 kB)

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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.

[1] Harman, R., Bachratá A., Filová L. 2015

Construction of efficient experimental designs under multiple resource constrains

[2] Bachratá, A., Harman, R. 2013

A stochastic optimization method for constructing optimal block designs with linear constraints