Application of Bayesian Method in Modeling Economic Processes

• Дата: 2025
• Автори: Радзієвська, Олена, Ковальська, Ірина
• Формат: Стаття
• Мова: Ukrainian
• Опубліковано: Кам'янець-Подільський національний університет імені Івана Огієнка 2025
• Онлайн доступ: http://mcm-math.kpnu.edu.ua/article/view/334840
• Назва журналу: Mathematical and computer modelling. Series: Physical and mathematical sciences

In the modern world, data is one of the most important resources. The ability to effectively analyze them and draw informed conclusions is becoming key. Bayesian methods, the basis of which is Bayes' theorem, offer a powerful and flexible tool for solving complex problems, allowing you to update your initial ideas in the light of new evidence. The methods are based on the concept of posterior probability and the use of Bayes' formula, and Bayes' probability is considered as the degree of confidence in the corresponding event. Bayes' theorem, in essence, is a formalization of how you can learn from experience. It provides a mathematical apparatus for combining prior knowledge (or «prior» beliefs) with data obtained from the real world to form more accurate and reliable «posterior» conclusions. This makes Bayesian methods particularly valuable in areas where uncertainty is an inherent part of the process, as well as where decisions need to be made under conditions of limited information. In this article, Bayes' theorem is used to model the posterior probability density function of some parameter – an unknown mathematical expectation (for example, the average percentage increase in household income in a given area). Let the average percentage increase in income be known from previous studies. If we randomly obtain a sample of n households, that is, a random sample x from the general population, which, let us assume, has a normal distribution with an unknown mathematical expectation and a known variance, then we can find the posterior probability density function of this parameter. To study the percentage income of households for the first quarter, a random sample of 10 households is selected. As a result, it is shown that the combination of additional information contained in only ten independent observations with a priori information led to a significant reduction in the uncertainty of the assumption regarding the parameter of the mathematical expectation.