Nonconjugate priors and Metropolis-Hastings algorithms

  • Peter D. Hoff
Part of the Springer Texts in Statistics book series (STS)


When conjugate or semiconjugate prior distributions are used, the posterior distribution can be approximated with the Monte Carlo method or the Gibbs sampler. In situations where a conjugate prior distribution is unavailable or undesirable, the full conditional distributions of the parameters do not have a standard form and the Gibbs sampler cannot be easily used. In this section we present the Metropolis-Hastings algorithm as a generic method of approximating the posterior distribution corresponding to any combination of prior distribution and sampling model. This section presents the algorithm in the context of two examples: The first involves Poisson regression, which is a type of generalized linear model. The second is a longitudinal regression model in which the observations are correlated over time.


Markov Chain Posterior Distribution Prior Distribution Gibbs Sampler Generalize Little Square 
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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of WashingtonSeattleUSA

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