Getting it right: Joint distribution tests of posterior simulators

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Journal Article
Journal of the American Statistical Association, 2004, 99 (467), pp. 799 - 804
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Analytical or coding, errors in posterior simulators can produce reasonable but incorrect approximations of posterior moments. This article develops simple tests of posterior simulators that detect both kinds of errors, and uses them to detect and correct errors in two previously published articles. The tests exploit the fact that a Bayesian model specifies the joint distribution of observables (data) and unobservables (parameters). There are two joint distribution simulators. The marginal-conditional simulator draws unobservables from the prior and then observables conditional on unobservables. The successive-conditional simulator alternates between the posterior simulator and an observables simulator. Formal comparison of moment approximations of the two simulators reveals existing analytical or coding errors in the posterior simulator.
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