Approximate Bayesian computation methods are useful for generative models with intractable likelihoods. These methods are, however, sensitive to the dimension of the parameter space, requiring exponentially increasing resources as this dimension grows. To tackle this difficulty we explore a Gibbs version of the approximate Bayesian computation approach that runs component-wise approximate Bayesian computation steps aimed at the corresponding conditional posterior distributions, and based on summary statistics of reduced dimensions. While lacking the standard justifications for the Gibbs sampler, the resulting Markov chain is shown to converge in distribution under some partial independence conditions. The associated stationary distribution can further be shown to be close to the true posterior distribution, and some hierarchical versions of the proposed mechanism enjoy a closed-form limiting distribution. Experiments also demonstrate the gain in efficiency brought by the Gibbs version over the standard solution.

中文翻译：

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通过类似 Gibbs 的步骤进行分量近似贝叶斯计算

近似贝叶斯计算方法对于具有难以处理的可能性的生成模型很有用。然而，这些方法对参数空间的维度很敏感，随着该维度的增长，需要的资源呈指数增长。为了解决这个困难，我们探索了近似贝叶斯计算方法的 Gibbs 版本，该方法运行针对相应条件后验分布的组件式近似贝叶斯计算步骤，并基于缩减维度的汇总统计。虽然缺乏吉布斯采样器的标准理由，但结果马尔可夫链显示在某些部分独立条件下分布收敛。相关的平稳分布可以进一步显示为接近真实的后验分布，并且所提出机制的一些分层版本享有封闭形式的限制分布。实验还证明了 Gibbs 版本比标准解决方案带来的效率提升。