Editorial: Model selection and efficiency—is ‘Which model …?’ the right question?
Editorial: Model selection and efficiency—is ‘Which model …?’ the right question?
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DOI：
10.1111/j.1467-985x.2005.00366.x
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发表时间：
2005-07
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影响因子：
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通讯作者：
N. Longford
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文献类型：
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作者：
N. Longford
统计作为一门科学和职业，在过去几十年中已经发生了变化，在计算技术革命的推动下，它的方向已经调整到为其他科学领域服务。因此，它涵盖了各种各样的活动，提供了广泛的职业，并被普遍认为是现代信息社会不可或缺的。这些积极的方面与深刻的弱点密切相关。我们无法就我们的主题的权威性定义、就其基本原则的简短清单达成一致（概率论的那些是不够的）或在特定环境中什么是良好做法，以及如何推广它。是一个实践的例子，随着强大的计算机和方便的软件使我们能够在更大的范围内探索数据，详细我们可以检查几个替代模型如何适合所研究的数据集，并确定其中之一。这种“最终”模型及其最大似然（ML）拟合（估计值和标准误差，或与之等效的信息）是许多报告或手稿结果部分的核心，在确认满足必要的规律性条件后，伴随着模型检查和（近似）无偏性和渐近效率的声明。尽管被认为是值得尊敬的，但这种方法是有缺陷的，因为它忽略了模型不确定性的后果。自从德雷珀（1995）和查特菲尔德（1995）对这一问题进行了清晰的讨论以来，无论是研究还是实践都没有给予太多的关注。对于贝叶斯主义者来说，这个话题可以通过将de Finnetti（1974）（“每个概率都是条件的”）解释为“每个后验分布都是条件的”来建设性地提出。我们通常在所选模型上有条件地研究估计量的性质，排除所选模型可能无效的可能性。毕竟，模型选择是一个随机的（数据依赖的）过程，但（未知的）“好”模型是固定的，是研究现象的一个属性，不受我们的研究设计和数据收集过程的影响。模型选择迫使我们在不考虑过程中可能犯下的错误的后果的情况下做出决定。我们最终把所有的推理鸡蛋放在一个编织不均匀的篮子里。根据目的的不同，一种错误相对于另一种错误可能是无害的或灾难性的。这两种错误的条件概率在假设检验中得到控制，通常不能很好地说明它们的严重性。举例来说，考虑教科书平衡单因素方差分析（ANOVA）设置（组内正态性和等方差），其中在J =10个组中的每个组中具有K = 8个观测值，以及两个问题：
Statistics as a science and profession has been transformed over the last few decades by finetuning its orientation to serve other scientific fields, encouraged by the revolution in computing technology. As a result, it encompasses a vast variety of activities, provides a wide range of careers and is universally accepted as indispensable to the modern information society. These positive aspects go hand in hand with profound weaknesses. We cannot agree on an authoritative definition of our subject, on a short list of its fundamental principles (those of probability theory are insufficient) or on what amounts to good practice in particular settings, and how to promote it. Model selection, with the associated uncertainty, is an example of practice that is becoming increasingly problematic as powerful computers and convenient software enable us to explore data in ever greater detail. We can inspect how several alternative models fit the studied data set, and settle on one of them. Such a ‘final’ model and its maximum likelihood (ML) fit (estimates and standard errors, or information equivalent to them) is the centre-piece of the results section of many a report or manuscript, accompanied by model checking and claims of (approximate) unbiasedness and asymptotic efficiency, after confirming that the requisite regularity conditions have been satisfied. Despite being regarded as respectable, this approach is flawed because it ignores the consequences of model uncertainty. Since the lucid discussions by Draper (1995) and Chatfield (1995), neither research nor practice has paid much attention to this issue. To Bayesians, the topic might be broached constructively by paraphrasing de Finnetti (1974) (‘Every probability is conditional’) as ‘Every posterior distribution is conditional’. We usually study the properties of estimators conditionally on the selected model, ruling out the possibility that the selected model might not be valid. After all, the model selection is a random (data-dependent) process, but the (unknown) ‘good’ model is fixed, being a property of the studied phenomenon and oblivious to our study design and data collection process. Model selection forces us to make a decision without considering the consequences of the errors that may have been made in the process. We end up putting all our inferential eggs in one unevenly woven basket. Depending on the purpose, an error of one kind may be innocuous or disastrous relative to an error of another kind. The conditional probabilities of these two kinds of error, controlled in hypothesis testing, are often a poor indication of their gravity. By way of an example, consider the text-book balanced one-way analysis-of-variance (ANOVA) setting (normality and equal variances within groups) with K = 8 observations in each of J =10 groups, and two problems: