This paper reviews background and examples of Bayesian predictive synthesis (BPS), and develops details in a subset of BPS mixture models. BPS expands on standard Bayesian model uncertainty analysis for model mixing to provide a broader foundation for calibrating and combining predictive densities from multiple models or other sources. One main focus here is BPS as a framework for justifying and understanding generalized "linear opinion pools," where multiple predictive densities are combined with flexible mixing weights that depend on the forecast outcome itself, i.e., the setting of outcome-dependent model mixing. BPS also defines approaches to incorporating and exploiting dependencies across models defining forecasts, and to formally addressing the problem of model set incompleteness within the subjective Bayesian framework. In addition to an overview of general mixture-based BPS, new methodological developments for dynamic BPS -- involving calibration and pooling of sets of predictive distributions in a univariate time series setting -- are presented. These developments are exemplified in summaries of an analysis in a univariate financial time series study.

翻译：本文回顾了贝叶斯预测合成（BPS）的背景与若干实例，并详细阐述了BPS混合模型子集的具体内容。BPS在标准贝叶斯模型不确定性分析的基础上拓展了模型混合方法，为校准与合并来自多个模型或其他来源的预测密度提供了更广泛的基础。本文的一个核心关注点在于，将BPS作为论证和理解广义“线性意见池”的理论框架——其中，多个预测密度通过灵活且依赖于预测结果本身的混合权重进行合并，即结果依赖型模型混合的情形。BPS还定义了在预测模型中纳入并利用模型间依赖关系，以及在主观贝叶斯框架内正式处理模型集合不完整性问题的方法。除概述基于混合的一般性BPS外，本文还提出了动态BPS的新方法论进展——涉及在单变量时间序列背景下对预测分布集合进行校准与池化。这些进展通过一项单变量金融时间序列研究的分析总结加以例证。