ABSTRACT According to the general law of likelihood, the strength of statistical evidence for a hypothesis as opposed to its alternative is the ratio of their likelihoods, each maximized over the parameter of interest. Consider the problem of assessing the weight of evidence for each of several hypotheses. Under a realistic model with a free parameter for each alternative hypothesis, this leads to weighing evidence without any shrinkage toward a presumption of the truth of each null hypothesis. That lack of shrinkage can lead to many false positives in settings with large numbers of hypotheses. A related problem is that point hypotheses cannot have more support than their alternatives. Both problems may be solved by fusing the realistic model with a model of a more restricted parameter space for use with the general law of likelihood. Applying the proposed framework of model fusion to data sets from genomics and education yields intuitively reasonable weights of evidence.

中文翻译：

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似然范式中的模型融合和多重检验：收缩和支持点零假设的证据

摘要 根据似然的一般规律，一个假设的统计证据的强度与其替代方案相反，是它们的似然比，每个似然在感兴趣的参数上最大化。考虑评估几个假设中每一个的证据权重的问题。在每个替代假设都有一个自由参数的现实模型下，这会导致权衡证据，而不会对每个零假设的真实性进行任何缩减。在具有大量假设的环境中，缺乏收缩会导致许多误报。一个相关的问题是点假设不能比它们的替代方案有更多的支持。这两个问题都可以通过将现实模型与参数空间更受限的模型融合以与一般似然定律一起使用来解决。