论文标题
关于通过近似贝叶斯计算对顽固模型的预测推断
On predictive inference for intractable models via approximate Bayesian computation
论文作者
论文摘要
近似贝叶斯计算（ABC）通常用于参数估计和模型比较，用于基于棘手的模拟器模型，其可能性函数无法评估。在本文中，我们改为研究ABC作为预测推断的通用近似方法的可行性，特别是用于计算未来观察结果或缺少感兴趣数据的后验预测分布。我们考虑了针对此目标的三种互补的ABC方法，每个方法都基于可以从哪种棘手模型的预测密度进行采样的不同假设。只有从观察到的模型参数的观测数据和将来数据的仿真可以用于推断的情况，并且表明在这种情况下，理想的摘要统计量是最小的预测性，而不是仅仅是足够的（从普通意义上）。还研究了利用特定潜在变量表示的ABC预测方法。我们还展示了如何在所考虑的预测设置中使用常见的ABC采样算法。首先使用简单的时间序列模型来说明我们的主要结果，这些模型促进了分析处理，然后使用两个常见的棘手动态模型。
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.
