原因、假说选择与最佳解释推理（英文）

Causes, Hypothesis Selection, and Inference to the Best Explanation

科学哲学领域的方法论研究者提出了各种对"最佳解释","融贯性"或者"统合性"的概率测度。这些测度如果有用,至少在某些情况下依赖它们作解释性推理应该比因果推理中通常用的统计方法更准确。格拉斯(2012)发现,大多数此类测度在小样本的情况下都不优于通常统计方法中用的似然度(likelihood)或后验概率。此后,格拉斯(2013)比较了他定义的测度和后验概率对解决一类假说选择问题的优劣。在该类问题中,需要从一组互不相容且非此即彼的假说中择一,但假说的概率未知。他的结果显示,在似然度已知而主观的先验概率和真实的概率分布不同的情况下,如果样本很小,极大化他的测度选择假说可以比极大化后验概率更准确。本文在格拉斯的框架下探究一些一致的模型选择方法在有限样本下的准确性。笔者发现不同方法在准确性上的优劣依赖于真实假说的分布以及所采用的主观先验概率。虽然很多方法可能在所有设置下都不是最优,但也没有方法在所有设置下都是最优。笔者认为,如果对真实假说的分布和主观先验概率没有限定,讨论哪种方法在样本量不大的情况下能更准确的选出真假说意义不大。

Philosophical methodologists have offered a variety of probabilistic measures of ＂best explanation,＂ ＂coherence,＂ or ＂unification.＂ Whatever they are called, these proposals are only of interest if in some circumstances they improve accuracy of inference to explanations in comparison with standard statistical methods used in causal inference. Glass （2012） has shown that most such proposals do not improve on standard statistical methods for very small samples. Glass （2013） has introduced a learning paradigm in which there are unknown probabilities over mutually exclusive and exhaustive alternative hypotheses. When the likelihoods are known and with subjective prior probabilities chosen separately from the true probability distribution, he shows that hypothesis selection by maximizing his measure can be more accurate in very small samples than hypothesis selection by maximum posterior probability. We investigate the behavior of various asymptotically correct model selection criteria in this paradigm, and show, among other things, that the comparative accuracies of model selection criteria depend on the distributions of true hypotheses and of subjective priors. No method dominates in all circumstances. While many ＂best explanation＂ criteria may be inferior in all instances of the paradigm, when the goal is to find the truth in small to medium sized samples, debates over the superiority of posterior probability versus maximum likelihood versus alternative criteria are pointless without a specification of the distributions of true hypotheses and prior subjective probabilities.