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. 2025 Jun 14;26(1):kxaf012. doi: 10.1093/biostatistics/kxaf012

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© The Author 2025. Published by Oxford University Press.

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

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Fig. 1. — Calculating precision weights for individual observations. These data are from Invasive Ductal Carcinoma breast tissue analyzed with 10x Genomics Visium (10x Genomics 2022), hereafter referred to as “Ductal Breast.” A)–C) The square root of the residual standard deviations estimated using nearest neighbor Gaussian processes [ defined in (3)] are plotted against average logcount (). B) Same as A, except a spline curve is fitted to the data to estimate the gene-wise mean–variance relationship. C) Using the fitted spline curve, each predicted count value () is mapped to its corresponding square root standard deviation value using .

Inline graphic — Calculating precision weights for individual observations. These data are from Invasive Ductal Carcinoma breast tissue analyzed with 10x Genomics Visium (10x Genomics 2022), hereafter referred to as “Ductal Breast.” A)–C) The square root of the residual standard deviations estimated using nearest neighbor Gaussian processes [ defined in (3)] are plotted against average logcount (). B) Same as A, except a spline curve is fitted to the data to estimate the gene-wise mean–variance relationship. C) Using the fitted spline curve, each predicted count value () is mapped to its corresponding square root standard deviation value using .