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 practical situations, including cases involving nuisance parameters and non-/semi-parametric structure, along with a number of numerical illustrations.
翻译:贝叶斯推论要求具体说明单一、准确的先前分配,而常客推论则只包含一个空洞的先前分配,而常客推论则只包含一个空洞的先前分配。由于几乎所有真实世界应用都位于这两个极端之间的某个地方,因此需要采取新办法。这一系列文件开发了一个新的框架,提供有效和有效的统计推论、预测等,同时顾及部分的事先资料和较不精确的更笼统的指定模型。本文充实了一个一般推论模型结构,不仅产生测试、信任间隔等结果,而且有理想的误差率控制参数保障,而且还有利于对 de~Finati-s-ness-ness-loss 保证的有效概率推论。这里的关键技术新颖之处是所谓的外部匹配性近似于一般的不精确概率,它带来数据和部分先前依赖的可能性衡量方法,用于推断和预测。尽管发展中有一些可能不熟悉的不精确性概念,但结果是一个不直观的、可能性驱动框架,正如预期,它将与熟悉的拜伊斯和经常出现的极端情况下的不可靠的解决办法相符合。更重要的是,因此,拟议的框架的以往部分范围都包含了先前部分细节。