[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85150-en":3,"doc-seo-85150-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},85150,1374391974468,"Eden","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Neural Posterior Estimation for Inferring Weak Lensing Shear","Prevailing weak gravitational lensing shear inference chains detect galaxies, estimate ellipticities, and apply calibrations for image noise, selection bias, and model misspecification, making uncertainty propagation across stages difficult. The work proposes neural posterior estimation (NPE) as simulation-based inference, training a deep network to map simulated multiband images to a variational posterior over the underlying shear field. This integrates detection, deblending, measurement, and calibration into a single implicit step. Experiments on simulated constant-shear data show accurate, well-calibrated posteriors for both shear components amid blending, spatially varying PSFs, stars, and detector artifacts, given sufficient simulation fidelity.","arXiv :2607 .09867v1 [ astro-ph .IM] 10 Jul 2026  \nDraft version July 14, 2026  \nTypeset using LATEX twocolumn style in AASTeX7.0.1  \nNeural Posterior Estimation for Inferring Weak Lensing Shear  \nTim White  ,1 Dingrui Tao  ,1 Camille Avestruz 2 And Jeffrey Regier 1  \nThe LSST Dark Energy Science Collaboration  \n1 Department of Statistics, University of Michigan  \n2 Department of Physics, University of Michigan  \nABSTRACT  \nThe prevailing approach to inferring weak gravitational lensing shear from images involves detecting galaxies, estimating their ellipticities, and calibrating these estimates to correct for image noise, selection bias, and model misspecification. Characterizing the statistical model and assumptions underlying this pipeline is challenging, which makes it difficult to propagate uncertainty through its various stages. As an alternative, we propose to infer shear using neural posterior estimation (NPE), a type of simulation-based inference. We train a deep neural network to map a simulated multiband image to avariational distribution over the underlying shear field, thereby folding galaxy detection, deblending, measurement, and calibration into a single implicit inference step. Once trained, the network accounts for all features present in the simulated images, including potential sources of bias. In experiments on simulated constant-shear images with increasingly complex observational effects, NPE produces accurate and well-calibrated posterior approximations for both shear components in the presence of blended galaxies, spatially varying point spread functions, stars, and detector artifacts. These results demonstrate that NPE can be a viable shear estimation method in settings where all anticipated features and artifacts can be simulated, a requirement that will become increasingly feasible as simulation fidelity improves in the coming decades.  \nKeywords: Observational cosmology (1146)—Weak gravitational lensing (1797)—Astronomy image processing (2306)— Convolutional neural networks (1938)— Astrostatistics techniques  \n(1886)—Bayesian statistics (1900)  \n1. INTRODUCTION  \nWeak gravitational lensing refers to the spatially correlated distortion of the apparent shapes of distant galaxies by intervening matter. This matter curves spacetime, deflecting photon trajectories and inducing a subtle but measurable transformation of galaxy images. The resulting distortion field, typically parametrized by shear (i.e., anisotropic stretching) and convergence (i.e., isotropic scaling), encodes information about the projected intervening matter distribution, making weak lensing a powerful probe of the Universe’s large-scale structure (M. Bartelmann & P. Schneider 2001; M. Kilbinger 2015; S. Dodelson 2017; R. Mandelbaum 2018; J. Prat & D. Bacon 2026) .  \nStage IV surveys such as the Vera C. Rubin Observatory’s Legacy Survey of Space and Time (LSST; ˇZ . Ivezi´c et al. 2019), the Euclid Space Telescope (R. Laureijs et al. 2011), and the Nancy Grace Roman Space  \nTelescope (D. Spergel et al. 2015; R. Akeson et al. 2019; O. Dore et al. 2019) will survey billions of galaxies. Constraining cosmological parameters based on these surveys will require precise shear measurements.  \nPrecisely measuring shear is challenging due to numerous observational effects which, unless modeled or corrected for, induce systematic biases in shear estimates (B. Jain et al. 2006; R. Mandelbaum et al. 2015) . For example, point spread functions (PSFs) convolve galaxy images, diluting and distorting the shear signal (T. Zhang et al. 2022 , 2023; T. I. Liaudat et al. 2023) . The PSF typically varies across the telescope’s focal plane, which makes correcting for the resulting convolution challenging. Image noise further biases the shear signal in each exposure (P. Melchior & M. Viola 2012; A. Gurvich & R. Mandelbaum 2016), and correcting for this effect is challenging because exposures are typically combined, or “coadded”(R. Mandelbaum et al.  \n2 White ","cbCaib0lXW8g3M79","https://ap.wps.com/l/cbCaib0lXW8g3M79","pdf",4444047,3,1,17,"English","en",105,"# Introduction\n## Weak gravitational lensing and shear inference challenges\n## Conventional multistage shear estimation pipelines\n## Alternative probabilistic posterior approaches","[{\"question\":\"Why is propagating uncertainty difficult in the conventional weak-lensing shear inference pipeline?\",\"answer\":\"The conventional pipeline is split into multiple stages—detection, ellipticity measurement, and calibration—each affected by image noise, selection bias, and model misspecification, making joint uncertainty propagation across stages challenging.\"},{\"question\":\"How does neural posterior estimation (NPE) infer the weak-lensing shear field?\",\"answer\":\"NPE trains a deep neural network to map simulated multiband images to a variational posterior distribution over the underlying shear field, performing detection, deblending, measurement, and calibration in one implicit inference step.\"},{\"question\":\"What observational effects were included in the NPE experiments and how did the results perform?\",\"answer\":\"Experiments used simulated constant-shear images with increasingly complex effects, including blended galaxies, spatially varying PSFs, stars, and detector artifacts; NPE produced accurate and well-calibrated posterior approximations for both shear components.\"}]",1784201406,43,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"neural-posterior-estimation-for-inferring-weak-lensing-shear","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":20},"https://docshare.wps.com/document/research-report/",{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/neural-posterior-estimation-for-inferring-weak-lensing-shear/85150/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-24","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why is propagating uncertainty difficult in the conventional weak-lensing shear inference pipeline?","Question",{"text":75,"@type":76},"The conventional pipeline is split into multiple stages—detection, ellipticity measurement, and calibration—each affected by image noise, selection bias, and model misspecification, making joint uncertainty propagation across stages challenging.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does neural posterior estimation (NPE) infer the weak-lensing shear field?",{"text":80,"@type":76},"NPE trains a deep neural network to map simulated multiband images to a variational posterior distribution over the underlying shear field, performing detection, deblending, measurement, and calibration in one implicit inference step.",{"name":82,"@type":73,"acceptedAnswer":83},"What observational effects were included in the NPE experiments and how did the results perform?",{"text":84,"@type":76},"Experiments used simulated constant-shear images with increasingly complex effects, including blended galaxies, spatially varying PSFs, stars, and detector artifacts; 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