In this paper, we analysed classification rules under Bayesian decision theory. The setup we considered here is fairly general, which can represent all possible parametric models. The Bayes classification rule we investigated minimises the Bayes risk under general loss functions. Among the existing literatures, the 0-1 loss function appears most frequently, under which the Bayes classification rule is determined by the posterior predictive densities. Theoretically, we extended the Bernstein–von Mises theorem to the multiple-sample case. On this basis, the oracle property of Bayes classification rule has been discussed in detail, which refers to the convergence of the Bayes classification rule to the one built from the true distributions, as the sample size tends to infinity. Simulations show that the Bayes classification rules do have some advantages over the traditional classifiers, especially when the number of features approaches the sample size.

中文翻译：

---

分类问题的贝叶斯决策规则

在本文中，我们分析了贝叶斯决策理论下的分类规则。我们在这里考虑的设置相当通用，可以代表所有可能的参数模型。我们研究的贝叶斯分类规则最小化了一般损失函数下的贝叶斯风险。现有文献中，0-1损失函数出现频率最高，其贝叶斯分类规则由后验预测密度决定。从理论上讲，我们将 Bernstein-von Mises 定理扩展到多样本情况。在此基础上，详细讨论了贝叶斯分类规则的预言性质，即随着样本量趋于无穷大，贝叶斯分类规则收敛于从真实分布构建的分类规则。