Bayesian Statistical Modelling
Bayesian Statistical Modelling
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DOI：
10.1198/004017002320256495
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发表时间：
2002-08
期刊：
影响因子：
2.5
通讯作者：
S. Ganocy
中科院分区：
文献类型：
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作者：
S. Ganocy
实现这些工具。第二部分给出了支持的发展。打印的表格和对CD-ROM的访问在第三部分中给出了执行这些方法所需的内容。在第四部分中进行了详细的案例研究，说明了表格所支持的数据分析范围。作者所陈述的目标——为不了解支持原则的外行提供统计方法——是值得称赞的。这些表格，无论是印刷的还是电子的，对于新手来说都很容易通过一步一步的例子来学习，特别是在第四部分中给出的。与此同时，知识渊博的用户应该得到一些关于方法论所依据的统计原理的解释。对这些问题的评论构成了本次审查的其余部分。设X为独立伯努利试验结果X4n5 D 6X11::: 1Xn7的样本空间，其参数为M p 2 601 17，值为p待确定，设XS D X1 C X2 C¢¢C Xn。程序原则上基于X4n5或XS，但在实践中基于XS。作者将其发展追溯到雅各布·伯努利（Jacob Bernoulli），并大量借鉴了耶日·内曼（Jerzy Neyman）的“科学统计”基础。作者在两个基本理由上打破了传统统计的排名：(1)M p的范围和(2)在通常由小到中等样本构成的实践中渐近性的使用。关于(1)，他们确凿地断言，用户可以准确地规定601 17的一个适当子集6p1 N p7，称为测量空间，其中M p是确定存在的。因此，他们寻求符合测量空间的推理问题的解决方案。使用XS=n的经典估计在给出通常不一致的值时存在严重缺陷。关于(2)，表格所依赖的计算机密集型发展基本上是精确的小样本。与称老鼠和大象的秤大致类似，每个测量空间对应着各种数据分析工具，如本报告第二段(a) - (d)所示，这些工具通过打印的表格和CD-ROM得到支持。技术发展始于双重问题：- 6p1 N p7中M p的测量区间和- X中的预测区域，置信水平¶，作为其可靠性的衡量标准。这些构成了“测量和预测空间”。其他方法建立在这些基础上。根据样本大小和置信水平，点估计关注于6p1 N p7中的-估计量。这些包括(a)“最小均方误差估计器”，设计用于最小化条件均方误差，给定-测量和预测空间，以及(b)“中点估计器”作为6p1 N p7中M p的-测量区间的中点。排除的目的，代替假设检验，是“证明M p的实际值p不同于6p1 N p7 6p1 N p7中的任何值，其中排除过程的可靠性是由显著性水平确定的。”因此，H0 2 M p 2 6p1 N p7被排除在6p1 N p7之外。似乎没有第二类错误，因为M p总是属于6p1 N p7，因此也没有排除过程的能力的概念。扩展表是计算机密集型优化算法的结果，该算法寻求每个标称可靠性水平的最优精度，同时减少由问题的离散性引起的多余可靠性。包含表明基于X4n5的程序优于基于XS的程序。尽管如此，由于明显的实际限制，可用的表使用XS。特别是，典型的输入变量有测量范围6p1 N p7、样本量N、置信水平、实现XS以及与排除相关的相关信息等。输出依次由测量间隔和用于评估数据的其他数量组成。支撑分析的原理表面上是非贝叶斯的。尽管如此，在作者的发展过程中，mp确实成为一个随机变量，主要是通过分配贝叶斯均匀先验超过6p1 np7。尽管对这些方法进行了仔细的开发，并为其实现提供了广泛的表格，但本审稿人认为它们的有效使用存在严重障碍。这些保留意见主要集中在假设测量范围6p1 N p7本身可以由用户准确规定。这种关注贯穿于科学方法的每一个阶段。新的实验，除非是严格的验证性的，会绘制出新的路径，因此过去关于早期测量空间的经验不需要在没有修改的情况下延续。争论的问题是范围的错误指定，这种错误指定的后果，以及程序对这种错误指定的可能的健壮性。作者对这些关键问题基本上保持沉默。因为如果参数范围太宽，那么作者对经典方法（基于M p 2 601175）的反对意见将逐字适用于他们自己的方法，但现在与实际（现在更小）的测量空间不一致。处方范围过窄的后果仍有待研究。另一方面，如果先前用户知识支持的范围足够窄，那么所有统计程序都变得没有意义。在他们的专著的早期，作者似乎同意以下观点：“如果统计学是一门应用学科，而不是数学的一个小分支，那么99%以上发表的论文都是无用的练习。”显然，《科学家和工程师二项分布手册》代表了他们为跻身另外1%所做的努力。我必须让其他用户的经验来判断这个目标实现得如何。
implementing these tools. Supporting developments are given in Part II. The printed tables and access to the CD-ROM are given in Part III as needed to implement the methods. Detailed case studies are developed in Part IV, illustrating the range of data analyses supported by the tables. The stated objectives—to offer statistical methodology for use by laymen outside the grasp of supporting principles—are achieved commendably by the authors. The tables, both printed and electronic, are easily accessed by the novice through a self-paced study following step-by-step examples, especially as given in Part IV. At the same time, knowledgeable users deserve some explanation as to the statistical principles on which the methodology rests. Comments on these issues constitute much of the remainder of this review. Let X be the sample space containing outcomes X4n5 D 6X11 : : : 1Xn7 of independent Bernoulli trials having parameter M p 2 601 17 with value p to be determined, and let XS D X1 C X2 C ¢ ¢ ¢ C Xn. Procedures are based in principle on either X4n5 or XS , but in practice on the latter. The authors trace developments back to Jacob Bernoulli, and draw heavily on the foundations of Jerzy Neyman for “scienti c statistics.” The authors break ranks with conventional statistics on two essential grounds: (1) the range of M p and (2) the use of asymptotics in a practice often typi ed by small to moderate samples. Regarding (1), they con dently assert that users can accurately stipulate a proper subset 6p1 N p7 of 601 17, called the measurement space, wherein M p is known to lie with certainty. Accordingly, they seek solutions to problems of inference that conform to the measurement space. Classical estimation using XS=n is faulted heavily here in giving often nonconforming values. With regard to (2), the computerintensive developments on which the tables rest are essentially exact for small samples. In rough analogy with scales for weighing mice and elephants, to each measurement space there corresponds a variety of data—analytic tools, listed as (a)–(d) in the second paragraph of this report, that are supported through the printed tables and the CD-ROM. Technical developments begin with the dual issues of ‚-measurement intervals for M p in 6p1 N p7 and ‚-prediction regions in X, with con dence level ¶ ‚ as a gauge of their reliability. These constitute the “‚-measurement & prediction space.” Other methods build on these. Point estimation focuses on ‚-estimators in 6p1 N p7 depending on the sample size as well as on the con dence level ‚. These include (a) the “minimum MSE ‚-estimator,” designed to minimize the conditional mean squared error, given the ‚-measurement & prediction space, and (b) the “midpoint ‚-estimator” as the midpoint of the ‚-measurement interval for M p in 6p1 N p7. The aim of exclusion, in lieu of hypothesis testing, is “to show that the actual value p of M p is different from any value in 6p1 N p7 6p1 N p7, where the reliability of the exclusion procedure is speci ed by the signi cance level .” Thus H0 2 M p 2 6p1 N p7 is excluded from 6p1 N p7. There appear to be no errors of the second kind, because M p always belongs to 6p1 N p7, and thus no concept of the power of an exclusion procedure to exclude. The extensive tables are the result of computer-intensive optimization algorithms seeking optimal precision for each nominal reliability level, while reducing excess reliability arising from discreteness of the problem. Procedures based on X4n5 are shown by inclusion to be superior to ones based on XS . Nonetheless, the available tables use XS owing to apparent practical constraints. In particular, typical input variables are the measurement range 6p1 N p7, the sample size n, the con dence level ‚, the realization XS , and allied information pertaining to exclusion, for example. Output in turn consists of ‚-measurement intervals and other quantities of use in assessing the data. Principles undergirding the analyses are ostensibly non-Bayesian. Nonetheless, M p does become a random variable during the course of the authors’ developments, essentially through the assignment of a Bayesian uniform prior over 6p1 N p7. Despite the careful development of these methodologies, and extensive tables for their implementation, this reviewer sees serious impediments to their effective use. These reservations focus largely on the assumption that the measurement range 6p1 N p7 can itself be stipulated accurately by users. This concern pervades every stage of the scienti c method. New experiments, unless strictly con rmatory, do chart new paths, so that past experience regarding earlier measurement spaces need not carry over without modi cation. At issue are problems with misspeci cation of the range, the consequences of such misspeci cation, and possible robustness of procedures to such misspeci cation. The authors essentially remain mute on these critical issues. For if the parameter range is cast too wide, then the authors’ objections to classical methods (based on M p 2 601175 apply verbatim to their own methods, but now with regard to nonconformity with the actual (now smaller) measurement space. Consequences of prescribing too narrow a range remain to be studied. On the other hand, if the range supported by prior user knowledge is suf ciently narrow, then all statistical procedures become moot. Early in their monograph the authors appear to subscribe to the following point of view: “ If statistics is an applied eld and not a minor branch of mathematics, then more than ninety-nine percent of the published papers are useless exercises.” Apparently, Binomial Distribution Handbook for Scientists and Engineers represents their efforts to be included in the other 1%. I must leave it to the experience of other users to judge how well this objective has been met.