Bayesian Reasoning in Data Analysis: A Critical Introduction
Bayesian Reasoning in Data Analysis: A Critical Introduction
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DOI：
10.1198/jasa.2004.s357
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发表时间：
2004-12
影响因子：
3.7
通讯作者：
G. Woodworth
中科院分区：
文献类型：
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作者：
G. Woodworth
在团队教学科学推理课程时，我偶然发现了Giulio D 'Agostini为物理学家和物理学学生撰写的关于贝叶斯科学推理的讲座和论文，所以很高兴看到这本书的出现。. .主要是写给物理学家和其他科学家的”（第vii页）。它加入了一个最近的书籍列表，如Spiegelhalter等人（2002），为高级学生和从业者写的。. .几乎可以肯定的是，在文章、书籍和媒体中，我们会越来越频繁地遇到“贝叶斯”一词。. .“（第vii页）。达戈斯蒂尼将他“自学成才”的转变追溯到1993年。他是一个热情的皈依者，正如他所说，“不断地，有时是讽刺地批评'传统'的统计方法。”像我们许多人一样，他“固执地批评这些传统的方法”，因为他觉得“被那些似乎意味着他们没有的东西的名字和方法欺骗了”（第9页）。阿门一位物理学家如是说。贝叶斯主义者对传统统计范式的非理性持续感到困惑，特别是在本科统计学“畅销书”中。令人困惑的是，任何人都可以面无表情地将概率定义为长期相对频率，因为这相当于将概率定义为相对频率的概率极限（或者，如果你愿意的话，几乎确定的极限），这就像将人类定义为人类的后代一样循环。同样令人困惑的是，任何人都可以严肃地声称，给定一个假设的数据概率与给定数据的假设概率具有一致的关系。当然，传统的统计推理声称不理解假设概率的概念。然而，正如达戈斯蒂尼所指出的，在某些情况下，例如诊断测试，频率论者愿意为假设分配概率，在这些情况下，第一类错误的概率与假设的证据权重完全无关。3.12.1）。当然，主观概率是答案;然而，在科学推理中对主观性的厌恶是带着燃烧的剑的天使，它将许多人从贝叶斯花园中排除。但正如达戈斯蒂尼和许多其他人所证明的那样，科学家们在解释观测结果时远非客观（Press and Tanur 2001）。达戈斯蒂尼曾写道，经验丰富的物理学家知道，观察是科学中唯一客观的东西;将观察转化为知识涉及许多隐含和明确的信念。然而，如果科学知识被理解为一个有充分支持的信念的网络，“具有与当前研究领域相对应的模糊边界”，那么某种形式的客观性就可以恢复。他的座右铭是“任何人都不应该被允许谈论客观性，除非他在前沿科学、经济学或任何其他应用领域拥有10-20年的经验”（D 'Agostini 1999）。传统的统计推理，其概率证伪的显著性检验范式，来自波普尔试图通过将科学推理建立在演绎推理的基础上来结束归纳问题;做出错误预测的理论在逻辑上是错误的。无论这个方案在一段时间内看起来多么整齐，“在实践中，一个单一的冲突或反例在方法论上永远不足以证伪一个理论”（Thornton 2002）。显著性检验是波普尔证伪的概率演绎，它已经被统计学家和科学家们雄辩地否定了，以至于人们惊讶于这个话题仍然作为统计推理的范式在大多数本科统计学入门教科书中教授（Parkhurst 1997）。毫不奇怪，在一两门传统的统计学课程之后，学生们开始将传统的统计实践视为某种自然和不言自明的，而事实上他们显然既不是。因此，统计教科书必须认真考虑从一开始就教授统计推理基础的必要性，即：
While team-teaching a course on scientific reasoning, I stumbled on Giulio D’Agostini’s lectures and papers on Bayesian scientific reasoning for physicists and physics students, so it is a great pleasure to see the appearance of this book “. . . primarily addressed to physicists and other scientists” (p. vii). It joins a list of recent books, such as that by Spiegelhalter et al. (2002), written for advanced students and practitioners “who . . . will almost certainly have encountered, with increasing frequency, the term ‘Bayesian’ in articles, books and the media . . . ” (p. vii). D’Agostini dates his “largely self-taught” transition to Bayesianism from 1993. He is a passionate convert, making, as he says, “continual, sometimes sarcastic, criticisms of ‘conventional’ statistical methods.” Like many of us, he is “doggedly critical of these conventional methods,” because he feels “cheated by names and methods which seem to mean something they do not” (p. ix). Amen. Thus spake a physicist. Bayesians are mystified by the irrational persistence of the conventional statistical paradigm, particularly in undergraduate statistics “best sellers.” It is baffling that anyone can with a straight face define probability as long-term relative frequency, because that amounts to defining probability as the probability limit (or, if you prefer, the almost certain limit) of a relative frequency, which is as circular as defining a human being as the offspring of human beings. It is equally baffling that anyone could seriously claim that the probability of data given a hypothesis has a consistent relationship with the probability of the hypothesis given the data. Of course, conventional statistical reasoning professes to not understand the idea of the probabilities of hypotheses. Nevertheless, as D’Agostini points out, there are situations, such as diagnostic testing, in which frequentists are willing to assign probabilities to hypotheses, and in those situations the probability of a type I error is utterly unrelated to the weight of evidence for the hypothesis (Sec. 3.12.1). Of course, subjective probability is the answer; however, an aversion to subjectivity in scientific reasoning is the angel with flaming sword that bars many from the Bayesian garden. But as D’Agostini and many others have demonstrated, scientists are far from objective in their interpretation of observations (Press and Tanur 2001). D’Agostini earlier wrote that experienced physicists know that observations are the only objective things in science; transforming observations into knowledge involves many implicit and explicit beliefs. However, a form of objectivity can be recovered if scientific knowledge is understood to be a network of well-supported beliefs, “with fuzzy borders which correspond to the areas of present research.” His motto is “no one should be allowed to speak about objectivity, unless he has had 10–20 years of experience in frontier science, economics, or any other applied field” (D’Agostini 1999). Conventional statistical reasoning, with its significance-testing paradigm of probabilistic falsification, derives from Popper’s attempt to make an end run around the problem of induction by basing scientific reasoning on deductive reasoning; theories that make false predictions are logically false. However tidy that scheme seemed for a time, “in practice a single conflicting or counterinstance is never sufficient methodologically to falsify a theory” (Thornton 2002). Significance testing, the probabilistic rendition of Popperian falsification, has been so eloquently discredited by statisticians and scientists of all stripes that one marvels that the topic is still taught in most introductory undergraduate statistics textbooks as the paradigm of statistical reasoning (Parkhurst 1997). It comes as no surprise that after a conventional statistics course or two, students come to view conventional statistical practices as somehow naturaland self-evident when in fact they are demonstrably neither. For that reason, statistics textbooks must take seriously the need to teach the foundations of statistical reasoning from the beginning, namely: