D – optimal plans in the case of a piecewise constant function

    Mathematical Modeling, Vol. 6 (2022), Issue 4, pg(s) 103-105

    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.