基于混合的非参数空间协方差函数估计及其在撒哈拉以南非洲HIV关键人群规模估计中的应用
Mixture-based Nonparametric Estimation of Spatial Covariance Functions with Applications to HIV Key Population Size Estimation across Sub-Saharan Africa
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中文总结 AI 辅助
本研究提出基于混合表示的非参数协方差函数估计方法，用于改进撒哈拉以南非洲女性性工作者人群规模的空间估计，以支持HIV资源分配。
中文摘要 AI 辅助
关于关键人群（如女性性工作者（FSWs））规模的可靠数据往往稀缺，尤其是在次国家级层面。准确的规模估计对于有效分配资源和实现HIV目标至关重要。由于FSW人群规模可能在各个区域间存在空间相关性，考虑空间依赖性的模型可以改进估计。此类模型的一个重要组成部分是协方差函数，它刻画了底层过程的空间依赖结构。在本研究中，我们研究空间协方差函数以估计撒哈拉以南非洲（SSA）的FSW人群规模。许多空间模型依赖于参数协方差函数。然而，参数估计可能遭受模型误设，可能导致低效或有偏的预测。因此，我们开发了一种稳健的非参数方法来估计$\mathbb{R}^d$中平稳各向同性过程的协方差函数。我们关注一类在所有维度中都有效的协方差函数，其中包括指数核和Matérn核等流行核。利用此类协方差函数可以表示为缩放高斯核的无限混合这一事实，我们提出了两种估计方法：加权最小二乘和非参数最大似然估计，以估计缩放高斯核的混合测度。我们还开发了使用非负最小二乘和二阶下降更新的计算高效方法来解决这些优化问题。我们通过模拟评估所提出的方法，并将其应用于估计SSA次国家级层面的FSW人群规模。
英文摘要
Consistent data on the sizes of key populations, such as female sex workers (FSWs), are often scarce, particularly at the sub-national level. Accurate size estimates are critical to effectively allocate resources and achieve HIV targets. Since FSW population sizes may be spatially correlated across areas, models that account for spatial dependence can improve estimation. An important component of such models is the covariance function, which characterizes the spatial dependence structure of the underlying process. In this work, we study spatial covariance functions to estimate FSW population sizes in Sub-Saharan Africa (SSA). Many spatial models rely on parametric covariance functions. However, parametric estimation can suffer from model mis-specification, potentially leading to inefficient or biased predictions. We therefore develop a robust non-parametric approach for estimating the covariance function of a stationary isotropic process in $\mathbb{R}^d$. We focus on a class of covariance functions that are valid in all dimensions, which includes popular kernels such as the exponential and Matérn kernels. Leveraging the fact that such covariance functions can be represented as infinite mixtures of scaled Gaussian kernels, we propose two estimation methods: weighted least squares and nonparametric maximum likelihood estimation to estimate the mixing measure of scaled Gaussian kernels. We also develop computationally efficient methods to solve these optimization problems using non-negative least squares and second-order descent updates. We evaluate the proposed methods through simulations and apply them to estimate the FSW population sizes at the sub-national level in SSA.
发表机构
- Pennsylvania State University（宾夕法尼亚州立大学）
机构由 AI 辅助整理，请以论文原文为准。
