BAYESIAN METHOD OF EVALUATING ALTERNATIVE SOLUTIONS

Abstract

Most modern economic and mathematical models are multicriteria optimization dynamic systems with predominantly stochastic parameters. The mathematical models of these systems are complex; the search for optimal control is ambiguous, both in terms of optimality criteria and in the choice of methods for evaluating selected alternatives. The limited sample data, the random nature of the model parameters are a characteristic feature of predictive models of the economy, respectively, the application of the methods of the classical asymptotic theory to them is not justified and not effective. The Bayesian approach considers randomness as an intrinsic property of a real object, or process, taking into account the continuous random changes of the object itself, as an integral system, due to the influence of the environment. The estimates of the model will not be random statistical characteristics that approximate the statistics of a random parameter rather closely. Therefore, in practical application, the researcher works with a model that has deterministic coefficients. The aim of the research is the algorithmization of the Bayesian estimation procedure for alternative solutions. Modeling is described as a step-by-step process that begins with the identification of empirical patterns of development of the object-object system, analysis of external and internal factors, their relationships, and trends in dynamic environmental change. The next step is a theoretical assumption about the internal logical model of behavior of the object under study, the presence of typical relationships between structural parts and the influence of the environment – the state of nature. The solution of such problems can be found by searching for elements of a set of alternatives, each of which with some probability can be the optimal solution depending on random states of nature. The Bayesian method of probabilistic estimation of alternatives allows building a rather simple and effective model of decision-making for the formed set of a priori features – states of nature. The choice of methods for forming the distribution of a priori probabilities is not limited to statistical algorithms, for economic and mathematical models the easiest to implement is the method of expert estimates. A significant advantage of the Bayesian method is the ability to adjust and refine the initial values of a priori probabilities, in the event of new information about the object of study.