Dimensional Reduction for Sampled Priors and Application to Photometric Redshift Distributions
Year: 2026
Type: article
Abstract: A typical Bayesian inference on the values of some parameters of interest q from some data D involves running a Markov Chain (MC) to sample from the posterior p ( q , n ∣ D ) ∝ L ( D ∣ q , n ) p ( q ) p ( n ) , where n are some nuisance parameters with a separable prior. In some cases, the nuisance parameters are high-dimensional, and their prior p ( n ) is itself defined only by a set of samples that have been drawn from some other MC. The MC for the posterior will typically require evaluation of p ( n ) at arbitrary values of n , i.e., one needs to provide a density estimator over the full n space from the provided samples. But the high dimensionality of n hinders both the density estimation and the efficiency of the MC for the posterior. We describe a solution to this problem: a linear compression of the n space into a much lower-dimensional space u , which projects away directions in n space that cannot appreciably alter L . The algorithm for doing so is a slight modification to principal components analysis, and is less restrictive on p ( n ) than other proposed solutions to this issue. We demonstrate this “mode projection” technique using the analysis of 2-point correlation functions of weak lensing fields and galaxy density in the Dark Energy Survey, where n is a binned representation of the redshift distribution n ( z ) of the galaxies.
Source: The Astrophysical Journal
Authors: G. M. Bernstein, W. d’Assignies, M. A. Troxel, A. Alarcon, A. Amon, G. Giannini, B. Yin, M. Aguena, S. S. Allam, F. Andrade-Oliveira, D. Brooks, A. Carnero Rosell, J. Carretero, L. N. da Costa, M. E. S. Pereira, J. De Vicente, S. Everett, J. Frieman, J. García-Bellido, D. Gruen, S. R. Hinton, D. L. Hollowood, K. Honscheid, D. J. James, S. Lee, J. L. Marshall, J. Mena-Fernández, R. Miquel, A. A. Plazas Malagón, E. Sanchez, D. Sanchez Cid, I. Sevilla-Noarbe, T. Shin, M. Smith, E. Suchyta, M. E. C. Swanson, N. Weaverdyck, J. Weller, P. Wiseman
Institutions: University of Pennsylvania, Institute for High Energy Physics, Barcelona Institute of Science and Technology, Duke University, Institute of Space Sciences, Princeton University, University of Chicago, Laboratório Interinstitucional de e-Astronomia, Fermi National Accelerator Laboratory, University of Zurich, University College London, Universidad de La Laguna, Instituto de Astrofísica de Canarias, Universität Hamburg, Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas, California Institute of Technology, Consejo Superior de Investigaciones Científicas, Instituto de Física Teórica, Universidad Autónoma de Madrid, Ludwig-Maximilians-Universität München, The University of Queensland, University of California, Santa Cruz, The Ohio State University, Center for Astrophysics Harvard & Smithsonian, Jet Propulsion Laboratory, Texas A&M University, Centre National de la Recherche Scientifique, Institut National de Physique Nucléaire et de Physique des Particules, Université Grenoble Alpes, Institució Catalana de Recerca i Estudis Avançats, SLAC National Accelerator Laboratory, Kavli Institute for Particle Astrophysics and Cosmology, Stanford University, Stony Brook University, Lancaster University, Oak Ridge National Laboratory, National Center for Supercomputing Applications, Lawrence Berkeley National Laboratory, University of California, Berkeley, Max Planck Institute for Extraterrestrial Physics, University of Southampton
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $4,499
Funders: National Science Foundation, U.S. Department of Energy, University of Pennsylvania, Ohio State University, University of Chicago, University of Portsmouth, Centres de Recerca de Catalunya, University College London, European Commission, University of Sussex, Deutsche Forschungsgemeinschaft, Generalitat de Catalunya, Ministério da Ciência, Tecnologia e Inovação, Conselho Nacional de Desenvolvimento Científico e Tecnológico, Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro, Financiadora de Estudos e Projetos, Ministerio de Ciencia e Innovación, Institut de Física d'Altes Energies, University of Illinois at Urbana-Champaign, Office of Science, Science and Technology Facilities Council, Agència de Gestió d'Ajuts Universitaris i de Recerca, European Regional Development Fund, Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas, High Energy Physics, Integrated Electronics Engineering Center, Binghamton University, Argonne National Laboratory, Fermilab, Lawrence Berkeley National Laboratory, SLAC National Accelerator Laboratory
Awards: G1054097061, G1255325603, G1336129044, G1746333638, G179674260, G2011917337, G2233160401, G2290189609, G2376186588, G2554159582, G2636502879, G2673512141, G270620391, G302750986, G3154116105, G3215885808, G3261693824, G3439265645, G3496172001, G3522231704, G3690828678, G3803561910, The Dark Energy Survey Data Management Operations, G3870743921, G3906089732, G4019291869, G4027194468, G454676879, Collaborative Research: A gravitational inventory of the solar system using high precision minor planet astrometry, G4655338613, G4944594896, G5094610163, G5574724152, RESEARCH IN HIGH ENERGY PHYSICS AT THE UNIVERSITY OF PENNSYLVANIA, G5601225551, G5955501538, G6471802762, G6513613686, G656518222, G6676276723, G6941735741, G7425137858, G7731791180, G7788408655, G7824355187, G7835623888, G7915813472, G8284171658, Collaborative Research: The Dark Energy Survey Data Management Operations, G8920660035, G946511789
OpenAlex ID: W7157168794