论文标题
截短多元正常先验的质量转移现象
Mass-shifting phenomenon of truncated multivariate normal priors
论文作者
论文摘要
我们表明，截断为正矫正的依赖零均值正常分布的低维边密密度表现出质量转移现象。尽管截短的多元正常密度在原点处具有模式，但随着尺寸的增加，边缘密度在原点附近分配了越来越小的质量。这种现象在随机变量之间具有更强的相关性突出。提供了表征维度以及依赖性作用的精确量化。这种令人惊讶的行为对贝叶斯约束的估计和推断具有严重的影响，除了拥有全部支持之外，还需要在原点附近分配一个实质性的概率，以捕获感兴趣的真实功能的部分。没有进一步的修改，我们表明，截断的正常先验不适合在区域建模，并提出了一种基于使用乘法比例参数缩小坐标的新型替代策略。拟议的收缩先验在经验上被证明可以防止质量转移现象，同时保持计算效率。
We show that lower-dimensional marginal densities of dependent zero-mean normal distributions truncated to the positive orthant exhibit a mass-shifting phenomenon. Despite the truncated multivariate normal density having a mode at the origin, the marginal density assigns increasingly small mass near the origin as the dimension increases. The phenomenon accentuates with stronger correlation between the random variables. A precise quantification characterizing the role of the dimension as well as the dependence is provided. This surprising behavior has serious implications towards Bayesian constrained estimation and inference, where the prior, in addition to having a full support, is required to assign a substantial probability near the origin to capture at parts of the true function of interest. Without further modification, we show that truncated normal priors are not suitable for modeling at regions and propose a novel alternative strategy based on shrinking the coordinates using a multiplicative scale parameter. The proposed shrinkage prior is empirically shown to guard against the mass shifting phenomenon while retaining computational efficiency.
