| Abstract [eng] |
Markov chain Monte Carlo adaptive methods by creating computationally effective algorithms for decision-making of data analysis with the given accuracy are analyzed in this dissertation. The tasks for estimation of parameters of the multivariate distributions which are constructed in hierarchical way (skew t distribution, Poisson-Gaussian model, stable symmetric vector law) are described and solved in this research. To create the adaptive MCMC procedure, the sequential generating method is applied for Monte Carlo samples, introducing rules for statistical termination and for sample size regulation of Markov chains. Statistical tasks, solved by this method, reveal characteristics of relevant computational problems including MCMC method. Effectiveness of the MCMC algorithms is analyzed by statistical modeling method, constructed in the dissertation. Tests made with sportsmen data and financial data of enterprises, belonging to health-care industry, confirmed that numerical properties of the method correspond to the theoretical model. The methods and algorithms created also are applied to construct the model for sociological data analysis. Tests of algorithms have shown that adaptive MCMC algorithm allows to obtain estimators of examined distribution parameters in lower number of chains, and reducing the volume of calculations approximately two times. The algorithms created in this dissertation can be used to test the systems of stochastic type and to solve other statistical tasks by MCMC method. |
