The sample-based Gibbs sampler has been the dominant method for approximating joint distribution from a collection of compatible full-conditional distributions. However for conditionally specified model, mixtures of incompatible full and non-full conditional distributions are the realities; but, their updating orders are hard to identified. We propose a new algorithm, the Iterative Conditional Replacement (ICR), that produces distributional approximations toward the stationary distributions, dispensing Markov chain entirely. ICR always converges, and it produces mutually stationary distributions, which will be consistent among one another when the conditional distributions are compatible. Examples show ICR to be superior in quality, while being more parallelizable and requiring little effort in monitoring its convergence. Last, we propose an ensemble approach to decide the final model.

翻译：基于样本的吉布斯采样器一直是利用一组兼容的全条件分布来近似联合分布的主要方法。然而，对于条件指定模型而言，兼容与不兼容的全条件及非全条件分布的混合是现实情况，但其更新顺序难以确定。我们提出了一种新算法——迭代条件替换（ICR），该算法无需构建马尔可夫链，即可生成趋向平稳分布的近似分布。ICR始终收敛，并产生相互平稳的分布；当条件分布兼容时，这些分布彼此一致。实例表明，ICR在质量上更优，同时具有更高的可并行性，且几乎无需监测收敛性。最后，我们提出了一种集成方法来确定最终模型。