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Features of Application of Monte Carlo Method with Markov Chain Algorithms in Bayesian Data Analysis

  • Peter Bidyuk
  • Yoshio Matsuki
  • Aleksandr GozhyjEmail author
  • Volodymyr Beglytsia
  • Irina Kalinina
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1080)

Abstract

The article discusses the algorithms of the Monte Carlo method with Markov chains (MCMC). These are the Metropolis-Hastings and Gibbs algorithms. Descriptions and the main features of the algorithms application are given. The MCMC methods are developed to model sets of vectors corresponding to multidimensional probability distributions. The main application of these methods and algorithms in Bayesian data analysis procedures is directed towards study of posterior distributions. The main procedures of Bayesian data analysis are considered and the features of the application of the Metropolis-Hastings and Gibbs algorithms with different types of input data are considered. Examples of application of the algorithms and methods for their evaluation are provided.

Keywords

Monte Carlo method with Markov chains Bayesian data analysis Metropolis-Hastings algorithm Gibbs algorithm 

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”kyivUkraine
  2. 2.Kyoto UniversityKyotoJapan
  3. 3.Petro Mohyla Black Sea National UniversityNikolaevUkraine

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