Bayesian methods are a popular choice for statistical inference in small-data regimes due to the regularization effect induced by the prior. In the context of density estimation, the standard nonparametric Bayesian approach is to target the posterior predictive of the Dirichlet process mixture model. In general, direct estimation of the posterior predictive is intractable and so methods typically resort to approximating the posterior distribution as an intermediate step. The recent development of quasi-Bayesian predictive copula updates, however, has made it possible to perform tractable predictive density estimation without the need for posterior approximation. Although these estimators are computationally appealing, they tend to struggle on non-smooth data distributions. This is due to the comparatively restrictive form of the likelihood models from which the proposed copula updates were derived. To address this shortcoming, we consider a Bayesian nonparametric model with an autoregressive likelihood decomposition and a Gaussian process prior. While the predictive update of such a model is typically intractable, we derive a quasi-Bayesian predictive update that achieves state-of-the-art results in small-data regimes.

翻译：贝叶斯方法由于先验引入的正则化效应，在小样本数据场景下的统计推断中广受欢迎。在密度估计领域，标准的非参数贝叶斯方法以狄利克雷过程混合模型的后验预测为目标。通常，后验预测的直接估计是难以处理的，因此现有方法通常以近似后验分布作为中间步骤。然而，近期发展的拟贝叶斯预测连接函数更新使得无需后验近似即可进行可处理的预测密度估计。尽管这些估计量在计算上具有吸引力，但它们往往难以处理非光滑数据分布。这源于推导连接函数更新时所采用的似然模型形式相对受限。为弥补这一不足，我们考虑采用具有自回归似然分解和高斯过程先验的贝叶斯非参数模型。虽然此类模型的预测更新通常难以处理，但我们推导出一种拟贝叶斯预测更新方法，该方法在小样本数据场景下达到了最优性能。