标题： 高斯-狄利克雷后验优势在顺序学习中 显示英文标题

标题： Gaussian-Dirichlet Posterior Dominance in Sequential Learning

摘要： 我们考虑从在[0,1]区间内的分类观测中进行顺序学习的问题。 我们在分类结果的狄利克雷后验和具有N(0,1)噪声的观测下的高斯后验之间建立了一个顺序关系。 我们证明，当给定至少两个观测值的相同数据时，分类分布的后验均值将始终二阶随机支配高斯分布的后验均值。 这些结果为在分类结果下的顺序学习分析提供了一个有用的工具。 显示英文摘要

摘要： We consider the problem of sequential learning from categorical observations bounded in [0,1]. We establish an ordering between the Dirichlet posterior over categorical outcomes and a Gaussian posterior under observations with N(0,1) noise. We establish that, conditioned upon identical data with at least two observations, the posterior mean of the categorical distribution will always second-order stochastically dominate the posterior mean of the Gaussian distribution. These results provide a useful tool for the analysis of sequential learning under categorical outcomes.