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Bayesian computational methods

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  • Robert, Christian P.

Abstract

If, in the mid 1980?s, one had asked the average statistician about the difficulties of using Bayesian Statistics, his/her most likely answer would have been ?Well, there is this problem of selecting a prior distribution and then, even if one agrees on the prior, the whole Bayesian inference is simply impossible to implement in practice!? The same question asked in the 21th Century does not produce the same reply, but rather a much less serious complaint about the lack of generic software (besides winBUGS)! The last 15 years have indeed seen a tremendous change in the way Bayesian Statistics are perceived, both by mathematical statisticians and by applied statisticians and the impetus behind this change has been a prodigious leap-forward in the computational abilities. The availability of very powerful approximation methods has correlatively freed Bayesian modelling, in terms of both model scope and prior modelling. As discussed below, a most successful illustration of this gained freedom can be seen in Bayesian model choice, which was only emerging at the beginning of the MCMC era, for lack of appropriate computational tools. In this chapter, we will first present the most standard computational challenges met in Bayesian Statistics (Section 2), and then relate these problems with computational solutions. Of course, this chapter is only a terse introduction to the problems and solutions related to Bayesian computations. For more complete references, see Robert and Casella (1999, 2004) and Liu (2001), among others. We also restrain from providing an introduction to Bayesian Statistics per se and for comprehensive coverage, address the reader to Robert (2001), (again) among others.

Suggested Citation

  • Robert, Christian P., 2004. "Bayesian computational methods," Papers 2004,18, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
  • Handle: RePEc:zbw:caseps:200418
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    References listed on IDEAS

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    1. John Geweke, 1999. "Using simulation methods for bayesian econometric models: inference, development,and communication," Econometric Reviews, Taylor & Francis Journals, vol. 18(1), pages 1-73.
    2. John Geweke, 1999. "Using Simulation Methods for Bayesian Econometric Models," Computing in Economics and Finance 1999 832, Society for Computational Economics.
    3. Sylvia. Richardson & Peter J. Green, 1997. "On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 731-792.
    4. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
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    1. Richter, Matthias & Erhart, Michael & Vereecken, Carine A. & Zambon, Alessio & Boyce, William & Gabhainn, Saoirse Nic, 2009. "The role of behavioural factors in explaining socio-economic differences in adolescent health: A multilevel study in 33 countries," Social Science & Medicine, Elsevier, vol. 69(3), pages 396-403, August.

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