THEORETICAL FOUNDATIONS AND SPECIFICITY OF MATHEMATICAL MODELLING
D – optimal plans in the case of a piecewise constant function
- ^{1} L.N. Gumilyov Eurasian National University, Astana, Kazakhstan
Abstract
It is known that a large number of algorithms of the Monte Carlo method and experiment planning are based on the choice of a
certain probability distribution ρ.
This probability distribution ρ is given on a measurable space (X, B). And a given measurable space (X, B) has a density ρ(x) = dρ/dν by
some σ-finite measure v on (X,B).
When choosing a probability distribution ρ, the problem of solving the problem of finding the optimal density ρ arises.
As a result of solving the tasks, an explicit form of the Least squares Method of unknown parameters and variance was obtained. The
criterion of D – optimality is considered.
The D-optimal plans considered in this article are well known due to an important class of efficiency functions. To compare plans in terms of
D-optimality, the effectiveness of an arbitrary plan relative to the optimal plan is determined.
Thus, this article is devoted to the analysis of methods for constructing D-optimal experimental plans, where the basic object is a piecewise
constant function.
Keywords
References
- Ермаков С.М. Метод Монте-Карло и смежные вопросы. М. Наука, 1975 г.
- Ермаков С.М., Жиглявский А.А. Математическая теория оптимального эксперимента. М. Наука, 1987 г.
- Адамов А.А. Оптимальное рандомизованное планирование эксперимента. Автореферат на соиск. к.ф.-м.н. г.Ленинград, 1988