That science and other domains are now largely data-driven means virtually unlimited opportunities for statisticians. With great power comes responsibility, so it's imperative that statisticians ensure that the methods being developing to solve these problems are reliable. But reliable in what sense? This question is problematic because different notions of reliability correspond to distinct statistical schools of thought, each with their own philosophy and methodology, often giving different answers in applications. To achieve the goal of reliably solving modern problems, I argue that a balance in the behavioral-statistical priorities is needed. Towards this, I make use of Fisher's "underworld of probability" to motivate a new property called invulnerability that, roughly, requires the statistician to avoid the risk of losing money in a long-run sense. Then I go on to make connections between invulnerability and the more familiar behaviorally- and statistically-motivated notions, namely coherence and (frequentist-style) validity.
翻译:科学及其他领域如今在很大程度上由数据驱动,这为统计学家带来了几乎无限的机会。权力越大,责任越大,因此统计学家必须确保正在开发用于解决这些问题的方法是可靠的。但究竟在何种意义上可靠?这个问题之所以棘手,是因为不同的可靠性概念对应着不同的统计学派,每派都有自己的哲学和方法论,在应用中常常给出不同的答案。为了实现可靠解决现代问题的目标,我认为需要在行为优先级与统计优先级之间取得平衡。为此,我借鉴费舍尔的“概率底层世界”来激发一种称为“无懈可击性”的新性质,该性质大致要求统计学家避免在长期意义上承担亏损的风险。随后,我将进一步探讨无懈可击性与更常见的行为驱动和统计驱动概念(即融惯性与(频率学派意义上的)有效性)之间的联系。