A New Unified MCMC Methods Toward Unified Statistics Theory by MCMC

Our new technology (unified statistics theory by MCMC) generates new knowledge as well as the computational tools to create that knowledge and forms new modern and emerging scientific field of information technology and of AI. Skillfully, the basic of finite Markov chains (all types and properties) for the great development of this book to form a comprehensive picture is presented. Three proposed algorithms are designed and executed in order to introduce a complete framework toward a new philosophy of a surely successful rigorous methods and theory of MCMC, of statistical inference about Markov chains, of multiple regression analysis, and of optimization. We propose the unified statistics (descriptive and inferential) theory by MCMC. Using this, we propose unique chromosomes method for optimization and obtain classification of chains, fixed points (nonparametric tests), all conditional multivariate normal distributions (parametric tests and multiple regression analysis) and stationary multivariate normal distributions. We can solve any too large dimensional deterministic and probabilistic (the grouping data, both continuous and discrete) problems and obtain all results as above.