ALGORITHM FOR ASSESSING THE QUALITY OF MULTIDIMENSIONAL EXPERIMENTAL DATA BASED ON STATISTICAL ANALYSIS OF MARKOV PROCESSES

Abstract

The article describes a real-time piecewise-stationary vector process with several states stipulated by the appearance of one or more components (research intervals) of the “intense signal” – a low-frequency trend. We have found a separable function equivalent to the process under study in order to determine the state of a random vector process by investigating the character and structure of relationships between the process components, when the finite-dimensional distributions of this process were a priori unknown. This function is represented as a projection of a random process defined in a probability space on a subspace of sample functions located at the smallest distance from the process. Then, according to projection theorem with the account of Markov property, it is possible to construct a H0: Pt(t + h) = Pt(t) statistical hypothesis, assuming that statistical characteristics of (t + h) components interconnection get no significant changes until the detection of an “intense signal” in t + h interval. It is known that the problem of finding the projection corresponds to the problem of finding the mean square regression coefficients. Statistical analysis allowed to find the procedure and get the Bayesian algorithm in order to determine the state of Markov vector process by regression analysis methods. The efficiency of proposed approach is demonstrated on a simple example.