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A Review of Bayesian Posterior Distribution Based on MCMC Methods

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Computing and Data Science (CONF-CDS 2021)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1513))

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Abstract

Bayesian inference plays an essential role in the development of mathematical theory, as an important component of statistical methods. The prior distribution, the likelihood function and the posterior distribution are used in Bayesian inference. A combination of the prior distribution and the likelihood function will represent the posterior distribution, where the background information decides the prior distribution, and the background information and the observed data together form the likelihood function. This paper presents the background of Bayesian inference, the main developments, and the challenges of computing the posterior distribution. It focuses on six MCMC-based methods, such as the Metropolis-Hastings algorithm, Gibbs sampler, Reversible Jump MCMC, Hamiltonian Monte Carlo, Adaptive Metropolis, and preconditioned Crank-Nicolson. The advantages, limitations and applications of each algorithm are also briefly described.

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Author information

Authors and Affiliations

  1. Free University Berlin, 14195, Berlin, Germany

    Zijun Li

Authors
  1. Zijun Li
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Correspondence to Zijun Li .

Editor information

Editors and Affiliations

  1. Chinese Academy of Sciences, Beijing, China

    Weijia Cao

  2. University of California, Los Angeles, CA, USA

    Aydogan Ozcan

  3. China Academy of Space Technology, Beijing, China

    Haidong Xie

  4. Chinese Academy of Sciences, Beijing, China

    Bei Guan

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Li, Z. (2021). A Review of Bayesian Posterior Distribution Based on MCMC Methods. In: Cao, W., Ozcan, A., Xie, H., Guan, B. (eds) Computing and Data Science. CONF-CDS 2021. Communications in Computer and Information Science, vol 1513. Springer, Singapore. https://doi.org/10.1007/978-981-16-8885-0_17

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  • DOI: https://doi.org/10.1007/978-981-16-8885-0_17

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-16-8884-3

  • Online ISBN: 978-981-16-8885-0

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