Analysis of random factors of the self-education process - A. A. Solodov (Открытое образование (Москва))
The aim of the study is the statistical description of the random factors of the self-educationт process, namely that stage of the process of continuous education, in which there is no meaningful impact on the student’s educational organization and the development of algorithms for estimating these factors. It is assumed that motivations of self-education are intrinsic factors that characterize the individual learner and external, associated with the changing environment and emerging challenges. Phenomena available for analysis a self-learning process (observed data) are events relevant to this process, which are modeled by points on the time axis, the number and position of which is assumed to be random. Each point can be mapped with the unknown and unobserved random or nonrandom factor (parameter) which affects the intensity of formation of dots. The purpose is to describe observable and unobservable data and developing algorithms for optimal evaluation. Further, such evaluations can be used for the individual characteristics of the process of self-study or for comparison of different students. For the analysis of statistical characteristics of the process of selfeducation applied mathematical apparatus of the theory of point random processes, which allows to determine the key statistical characteristics of unknown random factors of the process of self-education. The work consists of a logically complete model including the following components.• Study the basic statistical model of the appearance of points in the process of self-education in the form of a Poisson process, the only characteristic is the intensity of occurrence of events• Methods of testing the hypothesis about Poisson distribution of observed events.• Generalization of the basic model to the case where the intensity function depends on the time and unknown factor (variable) can be both random and not random. Such factors are interpreted as motivational factors, as directly affect the intensity of formation of dots.• Generalization of the basic model of a different type, when each random event is attributed to random or non-random number. These numbers are interpreted as a resource (price), which is consumed with the appearance of each event and are mapped to external factors selflearning process.For each private model provided optimal algorithms for estimating the relevant factors according to selected criteria, in the simplest cases, the analytical expressions are indicated. It is shown that for a random parameter that is not time-dependent sufficient statistics is the number of points on the observation interval, and for time-varying random parameter, we apply the algorithm of optimal linear fi ltering. For external factors of self-educationт process, expressions for mathematical expectation and dispersion are obtained.. Considered a numerical example of application of the theory, including computational experiment. The use of mathematical apparatus of random point processes allows us to formulate the model of the random factors of the process of selfeducation in the form of random sequence of points which are identified with some of the events that accompany the process of self-education. The fruitfulness of the approach is confi rmed by the fact that algorithms to determine all the basic statistical characteristics of all the considered types of random processes of the occurrence of events are indicated and for simple cases analytical expressions are obtained.