Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes, a new approach is needed. This series of papers develops a new framework that provides valid and efficient statistical inference, prediction, etc., while accommodating partial prior information and imprecisely-specified models more generally. This paper fleshes out a general inferential model construction that not only yields tests, confidence intervals, etc.~with desirable error rate control guarantees, but also facilitates valid probabilistic reasoning with de~Finetti-style no-sure-loss guarantees. The key technical novelty here is a so-called outer consonant approximation of a general imprecise probability which returns a data- and partial prior-dependent possibility measure to be used for inference and prediction. Despite some potentially unfamiliar imprecise-probabilistic concepts in the development, the result is an intuitive, likelihood-driven framework that will, as expected, agree with the familiar Bayesian and frequentist solutions in the respective extreme cases. More importantly, the proposed framework accommodates partial prior information where available and, therefore, leads to new solutions that were previously out of reach for both Bayesians and frequentists. Details are presented here for a wide range of examples, with more practical details to come in later installments.

翻译：贝叶斯推断要求指定单一且精确的先验分布，而频率学派推断仅能容纳无信息先验。由于现实世界中的几乎所有应用都介于这两个极端之间，因此需要一种新方法。本系列论文开发了一个新框架，在更一般地容纳部分先验信息和不精确指定模型的同时，提供有效且高效的统计推断、预测等。本文阐述了一种通用的推断模型构造方法，该方法不仅能够生成具有理想错误率控制保证的检验、置信区间等，还能通过德·菲内蒂式的无必然损失保证实现有效的概率推理。这里的关键技术新颖之处在于一种所谓的一般不精确概率的外部协合逼近，它产生一个依赖于数据和部分先验的可能性测度，用于推断和预测。尽管在推导过程中涉及一些可能不常见的不精确概率概念，其结果是一个直观的、以似然性为驱动的框架，正如预期，它将在各自的极端情况下与熟悉的贝叶斯和频率学派解保持一致。更重要的是，所提出的框架在可用时容纳部分先验信息，因此能够产生以前贝叶斯学派和频率学派都无法触及的新解。本文通过大量示例详细介绍了相关内容，更具体的实践细节将在后续文章中呈现。