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Statistics and Computing

, Volume 1, Issue 2, pp 105–117 | Cite as

Bayesian analysis of outlier problems using the Gibbs sampler

  • Isabella Verdinelli
  • Larry Wasserman
Papers

Abstract

We consider the Bayesian analysis of outlier models. We show that the Gibbs sampler brings considerable conceptual and computational simplicity to the problem of calculating posterior marginals. Although other techniques for finding posterior marginals are available, the Gibbs sampling approach is notable for its ease of implementation. Allowing the probability of an outlier to be unknown introduces an extra parameter into the model but this turns out to involve only minor modification to the algorithm. We illustrate these ideas using a contaminated Gaussian distribution, at-distribution, a contaminated binomial model and logistic regression.

Keywords

Contaminated normal Gibbs sampling Monte Carlo outliers posterior marginals 

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Copyright information

© Chapman & Hall 1991

Authors and Affiliations

  • Isabella Verdinelli
    • 1
    • 2
  • Larry Wasserman
    • 2
  1. 1.Department of StatisticsUniversity of RomeRomeItaly
  2. 2.Department of StatisticsCarnegie Mellon UniversityPittsburghUSA

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