Design of Experiments in Stochastic Dynamics
PhD thesis advisor:
Radoslav Harman, co-supervised by Andrej Pázman
PhD thesis - Full text
The Thesis deals with the design of experiments for processes described by
ferential equations. The traditional approach to designing experiments is
based on solving
a deterministic system with subsequent contamination by a white noise, which
not correspond to the reality. In contrast to the traditional approach, in
the Thesis we as-
sume a randomness to be an inherent element of the observed process. The
the stochastic model has a significant impact not only on the optimal
allocation of observa-
tions but also on the attainable amount of information.
The main result of the Thesis is two-fold: the first is an explicit closed
for of the asymp-
totic Fisher information matrix for linear stochastic differential
equations, which can be
used for computation of the ultimate efficiency of a design. On the one
hand, the ultimate
efficiency gives an assessment of how much a given design exhausts the
tion and whether an optimization of experiment is needed. On the other hand,
efficiency indicates whether the costs for performing another measurement
are adequate to
the gain in the amount of information. The second result of the Thesis is
the discussion of
the existence of optimal designs for linear stochastic differential
equations, which is essen-
tial for the most basic objective of in the theory of optimal designs, and
thus has theoretical
and also practical meaning.
The achieved results are put into contrast with some of the recent
results are partially extended to a broader class of stochastic differential
equations, and we
give a demonstration using the Gompertz growth model.
 Lacko V: Ultimate efficiency of experimental designs for Ornstein-Uhlenbeck type processes,
Journal of Statistical Planning and Inference (v tlaci)
 Pázman A, Lacko V (2012): Prednášky z regresných modelov:
Odhadovanie parametrov strednej hodnoty a štatistická optimalizácia experimentu,
Vydavatelstvo Univerzity Komenského, ISBN 978-80-223-3070-1.
 Lacko V (2012): Planning of experiments for a nonautonomous
Ornstein-Uhlenbeck process, Tatra Mountains Mathematical Publications 51, pp101-113.
 Lacko V, Harman R (2012): A conditional distribution approach to uniform
sampling on spheres and balls in Lp spaces, Metrika 75 (7), pp939-951.
 Harman R., Lacko V. (2010): On decompositional algorithms for uniform
sampling from n-spheres and n-balls, Journal of Multivariate Analysis 101 (10),