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Fast approximate Bayesian inference of HIV indicators using PCA adaptive Gauss-Hermite quadrature.

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Title: Fast approximate Bayesian inference of HIV indicators using PCA adaptive Gauss-Hermite quadrature.
Authors: Howes, Adam1 (AUTHOR) ath19@ic.ac.uk, Stringer, Alex2 (AUTHOR) alex.stringer@uwaterloo.ca, Flaxman, Seth R.3 (AUTHOR) seth.flaxman@cs.ox.ac.uk, Imai–Eaton, Jeffrey W.4 (AUTHOR) jeaton@hsph.harvard.edu
Source: Journal of Theoretical Biology. Feb2026, Vol. 618, pN.PAG-N.PAG. 1p.
Subjects: HIV, Bayesian analysis, Gaussian quadrature formulas, Sub-Saharan Africans, Spatial analysis (Statistics), Multivariate analysis
Geographic Terms: Malawi, Africa
Abstract: • District-level HIV indicators are estimated with high-dimensional spatial models. • Fast and accurate Bayesian inference methods are required for workshop setting. • We combine principal component analysis with adaptive Gauss-Hermite quadrature. • Reduction in posterior standard deviation error by 74 % against empirical Bayes. • Compatible with Template Model Builder R package. Naomi is a spatial evidence synthesis model used to produce district-level HIV epidemic indicators in sub-Saharan Africa. Multiple outcomes of policy interest, including HIV prevalence, HIV incidence, and antiretroviral therapy treatment coverage are jointly modelled using both household survey data and routinely reported health system data. The model is provided as a tool for countries to input their data to and generate estimates with during a yearly process supported by UNAIDS. Previously, inference has been conducted using empirical Bayes and a Gaussian approximation, implemented via the TMB R package. We propose a new inference method based on an extension of adaptive Gauss-Hermite quadrature to deal with more than 20 hyperparameters. Using data from Malawi, our method improves the accuracy of inferences for model parameters, while being substantially faster to run than Hamiltonian Monte Carlo with the No-U-Turn sampler. Our implementation leverages the existing TMB C++ template for the model's log-posterior, and is compatible with any model with such a template. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
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Abstract:• District-level HIV indicators are estimated with high-dimensional spatial models. • Fast and accurate Bayesian inference methods are required for workshop setting. • We combine principal component analysis with adaptive Gauss-Hermite quadrature. • Reduction in posterior standard deviation error by 74 % against empirical Bayes. • Compatible with Template Model Builder R package. Naomi is a spatial evidence synthesis model used to produce district-level HIV epidemic indicators in sub-Saharan Africa. Multiple outcomes of policy interest, including HIV prevalence, HIV incidence, and antiretroviral therapy treatment coverage are jointly modelled using both household survey data and routinely reported health system data. The model is provided as a tool for countries to input their data to and generate estimates with during a yearly process supported by UNAIDS. Previously, inference has been conducted using empirical Bayes and a Gaussian approximation, implemented via the TMB R package. We propose a new inference method based on an extension of adaptive Gauss-Hermite quadrature to deal with more than 20 hyperparameters. Using data from Malawi, our method improves the accuracy of inferences for model parameters, while being substantially faster to run than Hamiltonian Monte Carlo with the No-U-Turn sampler. Our implementation leverages the existing TMB C++ template for the model's log-posterior, and is compatible with any model with such a template. [ABSTRACT FROM AUTHOR]
ISSN:00225193
DOI:10.1016/j.jtbi.2025.112290