Dimensional reduction for sampled priors and application to photometric redshift distributions
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| Format: | Preprint |
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2025
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| author | Bernstein, Gary Doumerg, William Assignies Troxel, Michael A. Alarcon, Alex Amon, Alexandra Giannini, Giulia Yin, Boyan Allam, Sahar Andrade-Oliveira, Felipe Brooks, David Rosell, Aurelio Carnero Carretero, Jorge da Costa, Luiz Pereira, Maria Elidaiana da Silva De Vicente, Juan Everett, Spencer Frieman, Josh Garcia-Bellido, Juan Gruen, Daniel Hinton, Samuel Hollowood, Devon L. Honscheid, Klaus James, David Lee, Sujeong Marshall, Jennifer Mena-Fernández, Juan Miquel, Ramon Malagón, Andrés Plazas Sanchez, Eusebio Cid, David Sanchez Sevilla, Ignacio Shin, Tae-hyeon Smith, Mathew Suchyta, Eric Swanson, Molly Weaverdyck, Noah Weller, Jochen Wiseman, Philip |
| author_facet | Bernstein, Gary Doumerg, William Assignies Troxel, Michael A. Alarcon, Alex Amon, Alexandra Giannini, Giulia Yin, Boyan Allam, Sahar Andrade-Oliveira, Felipe Brooks, David Rosell, Aurelio Carnero Carretero, Jorge da Costa, Luiz Pereira, Maria Elidaiana da Silva De Vicente, Juan Everett, Spencer Frieman, Josh Garcia-Bellido, Juan Gruen, Daniel Hinton, Samuel Hollowood, Devon L. Honscheid, Klaus James, David Lee, Sujeong Marshall, Jennifer Mena-Fernández, Juan Miquel, Ramon Malagón, Andrés Plazas Sanchez, Eusebio Cid, David Sanchez Sevilla, Ignacio Shin, Tae-hyeon Smith, Mathew Suchyta, Eric Swanson, Molly Weaverdyck, Noah Weller, Jochen Wiseman, Philip |
| contents | A typical Bayesian inference on the values of some parameters of interest $\bf q$ from some data $D$ involves running a Markov Chain (MC) to sample from the posterior $p({\bf q},{\bf n} | D) \propto \mathcal{L}(D | {\bf q},{\bf n}) p({\bf q}) p({\bf n}),$ where $\bf n$ are some nuisance parameters with separable prior. In some cases, the nuisance parameters are high-dimensional, and their prior $p({\bf n})$ 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 $p({\bf n})$ at arbitrary values of ${\bf n},$ i.e.\ one needs to provide a density estimator over the full $\bf n$ space from the provided samples. But the high dimensionality of $\bf n$ 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 $\bf n$ space into a much lower-dimensional space $\bf u$ which projects away directions in $\bf n$ space that cannot appreciably alter $\mathcal{L}.$ The algorithm for doing so is a slight modification to principal components analysis, and is less restrictive on $p(\bf n)$ 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 \textit{Dark Energy Survey}, where $\bf n$ is a binned representation of the redshift distribution $n(z)$ of the galaxies. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_00758 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dimensional reduction for sampled priors and application to photometric redshift distributions Bernstein, Gary Doumerg, William Assignies Troxel, Michael A. Alarcon, Alex Amon, Alexandra Giannini, Giulia Yin, Boyan Allam, Sahar Andrade-Oliveira, Felipe Brooks, David Rosell, Aurelio Carnero Carretero, Jorge da Costa, Luiz Pereira, Maria Elidaiana da Silva De Vicente, Juan Everett, Spencer Frieman, Josh Garcia-Bellido, Juan Gruen, Daniel Hinton, Samuel Hollowood, Devon L. Honscheid, Klaus James, David Lee, Sujeong Marshall, Jennifer Mena-Fernández, Juan Miquel, Ramon Malagón, Andrés Plazas Sanchez, Eusebio Cid, David Sanchez Sevilla, Ignacio Shin, Tae-hyeon Smith, Mathew Suchyta, Eric Swanson, Molly Weaverdyck, Noah Weller, Jochen Wiseman, Philip Instrumentation and Methods for Astrophysics Cosmology and Nongalactic Astrophysics A typical Bayesian inference on the values of some parameters of interest $\bf q$ from some data $D$ involves running a Markov Chain (MC) to sample from the posterior $p({\bf q},{\bf n} | D) \propto \mathcal{L}(D | {\bf q},{\bf n}) p({\bf q}) p({\bf n}),$ where $\bf n$ are some nuisance parameters with separable prior. In some cases, the nuisance parameters are high-dimensional, and their prior $p({\bf n})$ 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 $p({\bf n})$ at arbitrary values of ${\bf n},$ i.e.\ one needs to provide a density estimator over the full $\bf n$ space from the provided samples. But the high dimensionality of $\bf n$ 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 $\bf n$ space into a much lower-dimensional space $\bf u$ which projects away directions in $\bf n$ space that cannot appreciably alter $\mathcal{L}.$ The algorithm for doing so is a slight modification to principal components analysis, and is less restrictive on $p(\bf n)$ 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 \textit{Dark Energy Survey}, where $\bf n$ is a binned representation of the redshift distribution $n(z)$ of the galaxies. |
| title | Dimensional reduction for sampled priors and application to photometric redshift distributions |
| topic | Instrumentation and Methods for Astrophysics Cosmology and Nongalactic Astrophysics |
| url | https://arxiv.org/abs/2506.00758 |