Bayesian Parameters Identification Based on Monte Carlo Numerical Algorithms in Problems of Constructing Multivariate Regression Models with Stochastic Errors Presented in Semiparametric Form

The aim of the work is the identification of parameters in nonlinear multidimensional models and distributions with a complex structure (mixture of distributions) for the case of small samples. Similar problems often arise in different areas, including Economy in particular to identify the moment of change in the regime of macroeconomic systems. A commonly accepted method for solving this problem is to use a family of EM-algorithms to find the maximum of the likelihood function. However, as a numerical optimization algorithm, it has a number of traditional shortcomings: "jamming" in a local extremum and high computational complexity in large-dimensional spaces. The Bayesian approach is used in the work: the optimization problem is solved for complete and marginal a posteriori functions of parameter densities, which in turn are modeled (sampled) using Monte Carlo methods based on Markov chains, in particular, the Metropolis-Hastings family algorithms. As a result, the Kullback-Leibler distance is minimized between sampled and true density functions. Such an approach makes it more likely to find a global extremum in the sampled density function, and therefore improve the quality of the estimates obtained. Another advantage of the approach is the greater informativity of a posteriori distributions in analyzing the quality of interpolation of models and less sensitivity to the dimension of the problem.