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Markov Chain Monte Carlo Algorithms for Bayesian Computation, a Survey and Some Generalisation

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Case Studies in Applied Bayesian Data Science

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2259))

Abstract

This chapter briefly recalls the major simulation based methods for conducting Bayesian computation, before focusing on partly deterministic Markov processes and a novel modification of the bouncy particle sampler that offers an interesting alternative when dealing with large datasets.

The source of this chapter appears in the PhD thesis of the first author, which he defended in 2018 at Université Paris Dauphine.

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Notes

  1. 1.

    Some of the material in this section was also used in the paper “Accelerating MCMC Algorithms”, written by Christian P. Robert, Víctor Elvira, Nick Tawn, and Wu Changye and published in WIRES (2018).

  2. 2.

    In order to keep the notations consistent, we still denote the target density by π, with the prior density denoted as π 0 and the sampling distribution of one observation x as p(x|θ). The dependence on the sample \(\mathcal {D}\) is not reported unless necessary.

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Author information

Authors and Affiliations

  1. Université Paris Dauphine PSL, Paris, France

    Wu Changye & Christian P. Robert

  2. University of Warwick, Coventry, UK

    Christian P. Robert

Authors
  1. Wu Changye
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  2. Christian P. Robert
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Corresponding author

Correspondence to Christian P. Robert .

Editor information

Editors and Affiliations

  1. Mathematical Sciences, Queensland University of Technology, Brisbane, QLD, Australia

    Kerrie L. Mengersen

  2. I2M, CNRS, Centrale Marseille, Aix-Marseille University, Marseille, France

    Pierre Pudlo

  3. CEREMADE, Université Paris Dauphine, Paris, France

    Christian P. Robert

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Changye, W., Robert, C.P. (2020). Markov Chain Monte Carlo Algorithms for Bayesian Computation, a Survey and Some Generalisation. In: Mengersen, K., Pudlo, P., Robert, C. (eds) Case Studies in Applied Bayesian Data Science. Lecture Notes in Mathematics, vol 2259. Springer, Cham. https://doi.org/10.1007/978-3-030-42553-1_4

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