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An Overview of the Bayesian Approach

  • Adrian F. M. Smith
Chapter
Part of the Topics in Safety, Reliability and Quality book series (TSRX, volume 1)

Abstract

A framework is provided for combining the background knowledge and judgement of the subject matter expert with experimental or on-line data. It is shown that the logic of decision making points to the Bayesian approach as the natural one to deal with the various issues. A detailed discussion of the Bayesian statistical methods is given. Some recent progress towards the computational implementation of Bayesian methods is received and illustrated.

Keywords

Posterior Distribution Credible Interval Posterior Density Prior Belief Prior Density 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. DeGroot, M.H. (1970), Optimal Statistical Decisions, McGraw—Hill.Google Scholar
  2. Gelfand, A.E. & Smith, A.F.M. (1990), Sampling based approaches to calculating marginal densities, Journal of the American Statistical Association, 85, 398–409.MathSciNetzbMATHCrossRefGoogle Scholar
  3. Lindley, D.V. (1985), Making Decisions(Second Edition), Wiley, New York.Google Scholar
  4. Naylor, J.C. & Smith, A.F.M. (1982), Applications of a method for the efficient computation of posterior distributions,. Applied Statistics, 31, 214–225.MathSciNetzbMATHCrossRefGoogle Scholar
  5. Rubin, D.B. (1988). Using the SIR algorithm to simulate posterior distributions. In: J.M. Bernardo et al. (Eds), Bayesian Statistics 3, Oxford University Press.Google Scholar
  6. Smith, A.F.M., Skene, J.E.H. & Naylor, J.C. (1987), Progress with numerical and graphical methods for practical Bayesian statistics, Statistician, 36, 75–82.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1991

Authors and Affiliations

  • Adrian F. M. Smith
    • 1
  1. 1.Department of MathematicsHuxley Building Imperial CollegeLondonUK

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