论文标题
贝叶斯的推断和预测正常分布的平均混合物
Bayesian inference and prediction for mean-mixtures of normal distributions
论文作者
论文摘要
我们研究了多元正常分布的平均混合物的预测密度估计量的常见风险特性，涉及\ Mathbb {r}^d $中的未知位置参数$θ\，其中包括多变量偏差正常分布。我们为贝叶斯后验和预测密度提供明确的表示，包括基准最小风险均衡度（MRE）密度，该密度是最小值和广义贝叶斯的，就$θ$的均匀密度而言。对于四个或更大的维度，我们获得了贝叶斯密度，这些密度在kullback-leibler损耗下均匀地改善了MRE密度。我们还提供插件类型的改进，调查对$θ$的某些类型的参数限制的含义，并根据数值评估说明并评论发现。
We study frequentist risk properties of predictive density estimators for mean mixtures of multivariate normal distributions, involving an unknown location parameter $θ\in \mathbb{R}^d$, and which include multivariate skew normal distributions. We provide explicit representations for Bayesian posterior and predictive densities, including the benchmark minimum risk equivariant (MRE) density, which is minimax and generalized Bayes with respect to an improper uniform density for $θ$. For four dimensions or more, we obtain Bayesian densities that improve uniformly on the MRE density under Kullback-Leibler loss. We also provide plug-in type improvements, investigate implications for certain type of parametric restrictions on $θ$, and illustrate and comment the findings based on numerical evaluations.
