Study of the interfaith relations development based on the mathematical apparatus of Markov processes.

A.S. Leontiev, K.V. Gusev, S.A. Golovin

Abstract


A sociological survey was conducted, including questions characterizing the level of religious consciousness of Russians and the state of interfaith relations in the country. Answers to questions concerning attitudes towards religion and beliefs of the respondents are presented in the form of flow matrices. Based on flow matrices, frequency distributions matrices are calculated, as well as matrices of transition probabilities. The elements of the transition matrices are practically independent of time and characterize the stable, formed inter-confessional relations in Russia. This circumstance makes it possible to carry out a formalized description of their development in the form of discrete Markov chains, for the study of which there is a well-developed mathematical apparatus. For a discrete, irreducible aperiodic Markov chain with a finite number of states, there always exist limiting state probabilities that do not depend on the initial state probability distribution. This fundamental property is used in the development of a methodology for studying interfaith relations. A technique for using Markov processes to predict the level of religious consciousness and interfaith relations in Russia is proposed. The transition matrices of discrete Markov processes are determined based on the results of a survey, and a procedure for regularizing the transition matrices is proposed, which makes it possible to significantly increase the accuracy of forecasts. Based on Markov models, predictive values of indicators characterizing the change in religious consciousness and interfaith relations were obtained, and interval estimates of the predictive values of these indicators were determined based on mathematical statistics methods.

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References


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