基于贝叶斯矩阵分解模型的跨年龄和时间人口分析
Bayesian Adaptive Tensor Smoothing for Multiway Demographic Counts
AI总结：
本文提出了一种贝叶斯矩阵分解模型，用于跨年龄和时间的人口分析，通过低维因素分解实现对复杂人口过程的准确建模与预测。
摘要：
分析跨多个群体、时间时期和年龄组收集的人口数据具有挑战性，因为高维性、群体间人口异质性和较小群体内的随机变异性相互作用。本文提出了一种贝叶斯矩阵分解模型来解决这些挑战。通过将计数数据矩阵分解为低维潜在年龄和时间因素的乘积，该模型实现了简洁的表示，从而减轻过拟合并保持计算可行性，即使涉及数百个群体时也是如此。信息先验强制年龄因素的平滑性，并允许时间因素的动态演变。开发了一种简单的马尔可夫链蒙特卡洛算法进行后验推断。将该模型应用于2002年至2023年奥地利区级迁移数据，展示了其仅使用传统人口分解模型所需参数的一小部分，就能准确重建复杂人口过程的能力。一项预测实验显示，所提出的模型在标准基准上表现一致优于。除了统计人口学外，该框架在涉及噪声、异质性和高维非高斯矩阵数据的应用中具有广阔前景。
英文摘要：
Demographic data are often collected across multiple dimensions such as time, age, subnational region, and sex. Modeling such data is challenging due to the interplay of high dimensionality, heterogeneity between groups, and stochastic variability within small groups. This paper proposes a Bayesian adaptive tensor smoothing model for multiway demographic counts that represents the latent log-rate array as a sum of rank-one components. Global-local shrinkage priors control the effective rank of the decomposition, the number of modes along which each component varies, and the smoothness that Gaussian process priors impose along ordered modes such as age and time. Posterior inference relies on a data augmentation Markov chain Monte Carlo algorithm that interweaves centered and noncentered parameterizations in every layer of the model to keep mixing satisfactory in large and sparse count arrays. Applied to Swedish county-level and sex-specific mortality from 1969 to 2024, the model recovers stable demographic surfaces and life table quantities from noisy small-population data. In cross-validation exercises, the method outperforms both canonical demographic benchmarks and existing count tensor factorizations.
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