Approximate Bayesian computation (ABC) is commonly used for parameter estimation and model comparison for intractable simulator-based models whose likelihood function cannot be evaluated. In this paper we instead investigate the feasibility of ABC as a generic approximate method for predictive inference, in particular, for computing the posterior predictive distribution of future observations or missing data of interest. We consider three complementary ABC approaches for this goal, each based on different assumptions regarding which predictive density of the intractable model can be sampled from. The case where only simulation from the joint density of the observed and future data given the model parameters can be used for inference is given particular attention and it is shown that the ideal summary statistic in this setting is minimal predictive sufficient instead of merely minimal sufficient (in the ordinary sense). An ABC prediction approach that takes advantage of a certain latent variable representation is also investigated. We additionally show how common ABC sampling algorithms can be used in the predictive settings considered. Our main results are first illustrated by using simple time-series models that facilitate analytical treatment, and later by using two common intractable dynamic models.
翻译:在本文中,我们所调查的是ABC作为预测性推断的通用近似方法的可行性,特别是用于计算未来观测或相关缺失数据的后方预测分布。我们考虑了这一目标的三种互补ABC方法,每种方法都基于不同的假设,即从哪一种预测性密度中可以抽取棘手模型的样本。我们的主要结果首先通过使用简单的时间序列模型加以说明,以便利分析处理,然后使用两种共同的可变模型加以说明。