Likelihood-free methods such as approximate Bayesian computation (ABC) have extended the reach of statistical inference to problems with computationally intractable likelihoods. Such approaches perform well for small-to-moderate dimensional problems, but suffer a curse of dimensionality in the number of model parameters. We introduce a likelihood-free approximate Gibbs sampler that naturally circumvents the dimensionality issue by focusing on lower-dimensional conditional distributions. These distributions are estimated by flexible regression models either before the sampler is run, or adaptively during sampler implementation. As a result, and in comparison to Metropolis-Hastings-based approaches, we are able to fit substantially more challenging statistical models than would otherwise be possible. We demonstrate the sampler’s performance via two simulated examples, and a real analysis of Airbnb rental prices using a intractable high-dimensional multivariate nonlinear state-space model with a 36-dimensional latent state observed on 365 time points, which presents a real challenge to standard ABC techniques.

中文翻译：

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无可能性的近似吉布斯采样

诸如近似贝叶斯计算（ABC）之类的无可能性方法已将统计推断的范围扩展到具有计算上难以解决的可能性的问题。这样的方法对于中小尺寸问题表现良好，但是在模型参数数量方面遭受了尺寸诅咒。我们介绍了一种无可能性的近似Gibbs采样器，该采样器通过关注低维条件分布自然地规避了维数问题。这些分布是在采样器运行之前或在采样器实施期间通过自适应回归模型估算的。结果，与基于Metropolis-Hastings的方法相比，我们能够拟合更具挑战性的统计模型。使用难处理的高维多元非线性状态空间模型以及在365个时间点观察到的36维潜在状态，对Airbnb的租金价格提出了挑战，这对标准ABC技术构成了真正的挑战。