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.
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Bidyuk, P., Matsuki, Y., Gozhyj, A., Beglytsia, V., Kalinina, I. (2020). Features of Application of Monte Carlo Method with Markov Chain Algorithms in Bayesian Data Analysis. In: Shakhovska, N., Medykovskyy, M.O. (eds) Advances in Intelligent Systems and Computing IV. CSIT 2019. Advances in Intelligent Systems and Computing, vol 1080. Springer, Cham. https://doi.org/10.1007/978-3-030-33695-0_25
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