Mixture-based Nonparametric Estimation of Spatial Covariance Functions with Applications to HIV Key Population Size Estimation across Sub-Saharan Africa

2026-09-09

AI Summary

本文针对撒哈拉以南非洲地区性工作者人群规模估计问题，提出了一种基于混合模型的非参数方法来估计空间协方差函数，以提高估计准确性。

Abstract

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.

Problem

• spatial covariance functions
• key population size estimation
• Sub-Saharan Africa
• female sex workers
• spatial dependence

Innovation

• non-parametric estimation
• spatial covariance functions
• infinite mixtures of scaled Gaussian kernels
• weighted least squares
• nonparametric maximum likelihood estimation