论文标题
本地自适应空间分位数平滑：在东京监视犯罪密度的应用
Locally Adaptive Spatial Quantile Smoothing: Application to Monitoring Crime Density in Tokyo
论文作者
论文摘要
潜在异质性下的空间趋势估计是提取空间特征和危害（例如犯罪活动）的重要问题。通过关注分位数，与诸如均值之类的常用摘要统计数据相比，它提供了有关分布的大量信息，它通常不仅估算平均趋势，而且还可以估算高（低）风险趋势。在本文中，我们提出了一种贝叶斯分位趋势过滤方法，以估计图表上分位数的非平稳趋势，并将其应用于2013年至2017年之间东京的犯罪数据。通过对多个观察案例进行建模，我们可以估计应用程序多年来空间犯罪趋势的潜在异质性。为了诱导局部适应性贝叶斯对趋势的推断，我们引入了一般的收缩先验图形差异。引入具有多元分布的所谓阴影先验，用于局部规模参数和不对称拉式分布的混合物表示，我们提供了一种简单的Gibbs采样算法来生成后样品。通过模拟研究证明了所提出方法的数值性能。
Spatial trend estimation under potential heterogeneity is an important problem to extract spatial characteristics and hazards such as criminal activity. By focusing on quantiles, which provide substantial information on distributions compared with commonly used summary statistics such as means, it is often useful to estimate not only the average trend but also the high (low) risk trend additionally. In this paper, we propose a Bayesian quantile trend filtering method to estimate the non-stationary trend of quantiles on graphs and apply it to crime data in Tokyo between 2013 and 2017. By modeling multiple observation cases, we can estimate the potential heterogeneity of spatial crime trends over multiple years in the application. To induce locally adaptive Bayesian inference on trends, we introduce general shrinkage priors for graph differences. Introducing so-called shadow priors with multivariate distribution for local scale parameters and mixture representation of the asymmetric Laplace distribution, we provide a simple Gibbs sampling algorithm to generate posterior samples. The numerical performance of the proposed method is demonstrated through simulation studies.
