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Abstract:
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Conditionally specified models have been widely used for spatial models, multiple imputations, etc. In many applications, the conditional distributions are either estimated from different data bases or supplied by experts, hence, they are often incompatible and thus there does not exist a unique joint distribution. Finding a nearly compatible distribution mathematically is known to be very difficult. Here, we propose the use of Gibbs sampler to create an ensemble of joint distributions with the final distribution being a weighted combination all of the stationary distributions in the ensemble. Several examples are used to illustrate the competitive performance of the Gibbs ensemble. The accuracy of Gibbs ensembles is on a par with the mathematically optimal distributions. This learning approach is efficient because it is self-guided and requires no tuning.
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