标题： 适当评分和充分性 显示英文标题

标题： Proper Scoring and Sufficiency

摘要： 对数评分和信息发散出现在信息论、统计学、统计力学和投资组合理论中。 我们证明了所有这些主题都涉及某种优化，这直接导致了Bregman发散的使用。 如果也满足充分条件，则Bregman发散必须与信息发散成比例。 在不同的应用领域中，充分条件具有截然不同的后果，而且通常不满足。 因此，可以利用充分条件来解释何时一个领域的结果可以直接从一个领域转移到另一个领域，以及何时会遇到差异。 显示英文摘要

摘要： Logarithmic score and information divergence appear in both information theory, statistics, statistical mechanics, and portfolio theory. We demonstrate that all these topics involve some kind of optimization that leads directly to the use of Bregman divergences. If a sufficiency condition is also fulfilled the Bregman divergence must be proportional to information divergence. The sufficiency condition has quite different consequences in the different areas of application, and often it is not fulfilled. Therefore the sufficiency condition can be used to explain when results from one area can be transferred directly from one area to another and when one will experience differences.