Department of Statistics and Department of Political Science, Columbia University, New York, New York 10027, USA.
Br J Math Stat Psychol. 2013 Feb;66(1):8-38. doi: 10.1111/j.2044-8317.2011.02037.x. Epub 2012 Feb 24.
A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the most successful forms of Bayesian statistics do not actually support that particular philosophy but rather accord much better with sophisticated forms of hypothetico-deductivism. We examine the actual role played by prior distributions in Bayesian models, and the crucial aspects of model checking and model revision, which fall outside the scope of Bayesian confirmation theory. We draw on the literature on the consistency of Bayesian updating and also on our experience of applied work in social science. Clarity about these matters should benefit not just philosophy of science, but also statistical practice. At best, the inductivist view has encouraged researchers to fit and compare models without checking them; at worst, theorists have actively discouraged practitioners from performing model checking because it does not fit into their framework.
一个在科学哲学领域有相当影响力的学派将贝叶斯推理与归纳推理，甚至理性本身等同起来，而贝叶斯统计学的兴起和实际成功似乎进一步加强了这一观点。我们认为，最成功的贝叶斯统计形式实际上并不支持这种特殊的哲学，而是更符合复杂的假说演绎主义形式。我们考察了先验分布在贝叶斯模型中所扮演的实际角色，以及模型检验和模型修正的关键方面，这些都超出了贝叶斯确认理论的范围。我们借鉴了关于贝叶斯更新一致性的文献，也借鉴了我们在社会科学应用工作中的经验。这些问题的明晰化不仅将有益于科学哲学，而且有益于统计实践。贝叶斯归纳主义观点最多只能鼓励研究人员在不进行检查的情况下拟合和比较模型；最糟糕的是，理论家们积极阻止实践者进行模型检查，因为这不符合他们的框架。
