Bayes Factors
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贝叶斯因子
- 研究问题
- 如何用贝叶斯因子量化支持科学假说的证据，并在模型比较、估计与预测中纳入外部信息和模型不确定性？
- 方法与思路
- 作者结合五个科学领域的应用，综述贝叶斯因子的解释、计算与近似方法，并讨论模型加权及先验敏感性分析。
- 材料陈述的贡献
- 摘要强调其可评价支持原假说的证据、比较非嵌套模型及处理模型不确定性，并介绍包括 BIC 在内的计算近似。
- 阅读关注点
- 应核对先验如何影响边际似然、BIC 近似的适用条件，以及模型权重用于估计和预测时的具体解释。
- 阅读边界
- 仅据 OpenAlex 索引摘要，稿件版本未注明，不能推断刊本变化；摘要未给出计算近似的误差界或各应用的完整结果。
原文摘要
In a 1935 paper and in his book Theory of Probability, Jeffreys developed a methodology for quantifying the evidence in favor of a scientific theory. The centerpiece was a number, now called the Bayes factor, which is the posterior odds of the null hypothesis when the prior probability on the null is one-half. Although there has been much discussion of Bayesian hypothesis testing in the context of criticism of P-values, less attention has been given to the Bayes factor as a practical tool of applied statistics. In this article we review and discuss the uses of Bayes factors in the context of five scientific applications in genetics, sports, ecology, sociology, and psychology. We emphasize the following points: •From Jeffreys' Bayesian viewpoint, the purpose of hypothesis testing is to evaluate the evidence in favor of a scientific theory.•Bayes factors offer a way of evaluating evidence in favor of a null hypothesis.•Bayes factors provide a way of incorporating external information into the evaluation of evidence about a hypothesis.•Bayes factors are very general and do not require alternative models to be nested.•Several techniques are available for computing Bayes factors, including asymptotic approximations that are easy to compute using the output from standard packages that maximize likelihoods.•In “nonstandard” statistical models that do not satisfy common regularity conditions, it can be technically simpler to calculate Bayes factors than to derive non-Bayesian significance tests.•The Schwarz criterion (or BIC) gives a rough approximation to the logarithm of the Bayes factor, which is easy to use and does not require evaluation of prior distributions.•When one is interested in estimation or prediction, Bayes factors may be converted to weights to be attached to various models so that a composite estimate or prediction may be obtained that takes account of structural or model uncertainty.•Algorithms have been proposed that allow model uncertainty to be taken into account when the class of models initially considered is very large.•Bayes factors are useful for guiding an evolutionary model-building process.•It is important, and feasible, to assess the sensitivity of conclusions to the prior distributions used.