Statistical Component Separation for Targeted Signal Recovery in Noisy Mixtures

Separating signals from an additive mixture may be an unnecessarily hard problem when one is only interested in specific properties of a given signal. In this work, we tackle simpler "statistical component separation" problems that focus on recovering a predefined set of statistical descriptors of a target signal from a noisy mixture. Assuming access to samples of the noise process, we investigate a method devised to match the statistics of the solution candidate corrupted by noise samples with those of the observed mixture. We first analyze the behavior of this method using simple examples with analytically tractable calculations. Then, we apply it in an image denoising context employing 1) wavelet-based descriptors, 2) ConvNet-based descriptors on astrophysics and ImageNet data. In the case of 1), we show that our method better recovers the descriptors of the target data than a standard denoising method in most situations. Additionally, despite not constructed for this purpose, it performs surprisingly well in terms of peak signal-to-noise ratio on full signal reconstruction. In comparison, representation 2) appears less suitable for image denoising. Finally, we extend this method by introducing a diffusive stepwise algorithm which gives a new perspective to the initial method and leads to promising results for image denoising under specific circumstances.Comment: 11+12 pages, 5+5 figures, code: https://github.com/bregaldo/stat_comp_se

Simulation based stacking

Simulation-based inference has been popular for amortized Bayesian computation. It is typical to have more than one posterior approximation, from different inference algorithms, different architectures, or simply the randomness of initialization and stochastic gradients. With a provable asymptotic guarantee, we present a general stacking framework to make use of all available posterior approximations. Our stacking method is able to combine densities, simulation draws, confidence intervals, and moments, and address the overall precision, calibration, coverage, and bias at the same time. We illustrate our method on several benchmark simulations and a challenging cosmological inference task

On the binding of N-acetylglucosamine and chitobiose to hen lysozyme in the solid state at high temperature

Copyright © 1979 Published by Elsevier Science B.V. All rights reserved.This paper deals with the crystallization of lysozyme at 40°C and 50°C in the presence of GlcNAc or chitobiose

Apport de la géostatistique à la connaissance de la morphologie naturelle du site de Bordeaux (France)

En site urbain, à la base des niveaux anthropisés, le paléorelief correspond globalement à la surface géologique naturelle la plus récente. La connaissance de cette surface est capitale pour comprendre les raisons et les modalités des implantations humaines (accessibilité et position du site par exemple). L’objectif poursuivi est d’utiliser les données de forages disponibles dans le cœur historique de Bordeaux, pour les intégrer dans un modèle 2,5D. L’un des éléments majeurs de cette problématique est la localisation et l’évolution des cours des deux principales rivières du centre ville que sont le Peugue et la Devèze. Un modèle a été construit sur le centre de Bordeaux, par krigeage sous contraintes d’inégalités en utilisant principalement les données litho-stratigraphiques des sondages géotechniques. Celui-ci permet de voir sous un jour nouveau l’évolution géomorphologique du centre ville historique et de montrer que l’image qu’avaient les archéologues sur l’hydrographie de ce secteur était incomplète.In urban location, paleorelief, below the anthropogenic surface, is the most recent natural geological layer. In order to understand the reasons and modalities of human implantations (site accessibility and location for example), it is capital to develop the knowledge of this surface. We have a database gathering many boreholes done in Bordeaux historical downtown. This database has been used for building a 2.5D model. A main question is the location and the evolution of the two main rivers of the town, the Peugue River and the Devèze River. This model has been built on Bordeaux town centre by using kriging under inequalities constraints provided by the litho-stratigraphic data of geotechnical boreholes. This model provides an innovative point of view about the geomorphological evolution of the town centre. It also shows that the representation the archaeologists had about historical evolution of the hydrography was incomplete

Sensitivity Analysis of Simulation-Based Inference for Galaxy Clustering

Simulation-based inference (SBI) is a promising approach to leverage high fidelity cosmological simulations and extract information from the non-Gaussian, non-linear scales that cannot be modeled analytically. However, scaling SBI to the next generation of cosmological surveys faces the computational challenge of requiring a large number of accurate simulations over a wide range of cosmologies, while simultaneously encompassing large cosmological volumes at high resolution. This challenge can potentially be mitigated by balancing the accuracy and computational cost for different components of the the forward model while ensuring robust inference. To guide our steps in this, we perform a sensitivity analysis of SBI for galaxy clustering on various components of the cosmological simulations: gravity model, halo-finder and the galaxy-halo distribution models (halo-occupation distribution, HOD). We infer the $\sigma_8$ and $\Omega_m$ using galaxy power spectrum multipoles and the bispectrum monopole assuming a galaxy number density expected from the luminous red galaxies observed using the Dark Energy Spectroscopy Instrument (DESI). We find that SBI is insensitive to changing gravity model between $N$-body simulations and particle mesh (PM) simulations. However, changing the halo-finder from friends-of-friends (FoF) to Rockstar can lead to biased estimate of $\sigma_8$ based on the bispectrum. For galaxy models, training SBI on more complex HOD leads to consistent inference for less complex HOD models, but SBI trained on simpler HOD models fails when applied to analyze data from a more complex HOD model. Based on our results, we discuss the outlook on cosmological simulations with a focus on applying SBI approaches to future galaxy surveys.Comment: 11 pages, 5 figures. Comments welcom

Cosmological Information in the Marked Power Spectrum of the Galaxy Field

Marked power spectra are two-point statistics of a marked field obtained by weighting each location with a function that depends on the local density around that point. We consider marked power spectra of the galaxy field in redshift space that up-weight low density regions, and perform a Fisher matrix analysis to assess the information content of this type of statistics using the Molino mock catalogs built upon the Quijote simulations. We identify four different ways to up-weight the galaxy field, and compare the Fisher information contained in their marked power spectra to the one of the standard galaxy power spectrum, when considering monopole and quadrupole of each statistic. Our results show that each of the four marked power spectra can tighten the standard power spectrum constraints on the cosmological parameters $\Omega_{\rm m}$, $\Omega_{\rm b}$, $h$, $n_s$, $M_\nu$ by $15-25\%$ and on $\sigma_8$ by a factor of 2. The same analysis performed by combining the standard and four marked power spectra shows a substantial improvement compared to the power spectrum constraints that is equal to a factor of 6 for $\sigma_8$ and $2.5-3$ for the other parameters. Our constraints may be conservative, since the galaxy number density in the Molino catalogs is much lower than the ones in future galaxy surveys, which will allow them to probe lower density regions of the large-scale structure.Comment: 19 pages, 12 figure

SIMBIG{\rm S{\scriptsize IM}BIG}: The First Cosmological Constraints from the Non-Linear Galaxy Bispectrum

We present the first cosmological constraints from analyzing higher-order galaxy clustering on non-linear scales. We use ${\rm S{\scriptsize IM}BIG}$, a forward modeling framework for galaxy clustering analyses that employs simulation-based inference to perform highly efficient cosmological inference using normalizing flows. It leverages the predictive power of high-fidelity simulations and robustly extracts cosmological information from regimes inaccessible with current standard analyses. In this work, we apply ${\rm S{\scriptsize IM}BIG}$ to a subset of the BOSS galaxy sample and analyze the redshift-space bispectrum monopole, $B_0(k_1, k_2, k_3)$, to $k_{\rm max}=0.5\,h/{\rm Mpc}$. We achieve 1$\sigma$ constraints of $\Omega_m=0.293^{+0.027}_{-0.027}$ and $\sigma_8= 0.783^{+0.040}_{-0.038}$, which are more than 1.2 and 2.4$\times$ tighter than constraints from standard power spectrum analyses of the same dataset. We also derive 1.4, 1.4, 1.7$\times$ tighter constraints on $\Omega_b$, $h$, $n_s$. This improvement comes from additional cosmological information in higher-order clustering on non-linear scales and, for $\sigma_8$, is equivalent to the gain expected from a standard analysis on a $\sim$4$\times$ larger galaxy sample. Even with our BOSS subsample, which only spans 10% of the full BOSS volume, we derive competitive constraints on the growth of structure: $S_8 = 0.774^{+0.056}_{-0.053}$. Our constraint is consistent with results from both cosmic microwave background and weak lensing. Combined with a $\omega_b$ prior from Big Bang Nucleosynthesis, we also derive a constraint on $H_0=67.6^{+2.2}_{-1.8}\,{\rm km\,s^{-1}\,Mpc^{-1}}$ that is consistent with early universe constraints.Comment: 13 pages, 7 figures, submitted to PRD, comments welcom

SIMBIG{\rm S{\scriptsize IM}BIG}: Mock Challenge for a Forward Modeling Approach to Galaxy Clustering

Simulation-Based Inference of Galaxies (${\rm S{\scriptsize IM}BIG}$) is a forward modeling framework for analyzing galaxy clustering using simulation-based inference. In this work, we present the ${\rm S{\scriptsize IM}BIG}$ forward model, which is designed to match the observed SDSS-III BOSS CMASS galaxy sample. The forward model is based on high-resolution ${\rm Q{\scriptsize UIJOTE}}$ $N$-body simulations and a flexible halo occupation model. It includes full survey realism and models observational systematics such as angular masking and fiber collisions. We present the "mock challenge" for validating the accuracy of posteriors inferred from ${\rm S{\scriptsize IM}BIG}$ using a suite of 1,500 test simulations constructed using forward models with a different $N$-body simulation, halo finder, and halo occupation prescription. As a demonstration of ${\rm S{\scriptsize IM}BIG}$, we analyze the power spectrum multipoles out to $k_{\rm max} = 0.5\,h/{\rm Mpc}$ and infer the posterior of $\Lambda$CDM cosmological and halo occupation parameters. Based on the mock challenge, we find that our constraints on $\Omega_m$ and $\sigma_8$ are unbiased, but conservative. Hence, the mock challenge demonstrates that ${\rm S{\scriptsize IM}BIG}$ provides a robust framework for inferring cosmological parameters from galaxy clustering on non-linear scales and a complete framework for handling observational systematics. In subsequent work, we will use ${\rm S{\scriptsize IM}BIG}$ to analyze summary statistics beyond the power spectrum including the bispectrum, marked power spectrum, skew spectrum, wavelet statistics, and field-level statistics.Comment: 28 pages, 6 figure

SIMBIG{\rm S{\scriptsize IM}BIG}: A Forward Modeling Approach To Analyzing Galaxy Clustering

We present the first-ever cosmological constraints from a simulation-based inference (SBI) analysis of galaxy clustering from the new ${\rm S{\scriptsize IM}BIG}$ forward modeling framework. ${\rm S{\scriptsize IM}BIG}$ leverages the predictive power of high-fidelity simulations and provides an inference framework that can extract cosmological information on small non-linear scales, inaccessible with standard analyses. In this work, we apply ${\rm S{\scriptsize IM}BIG}$ to the BOSS CMASS galaxy sample and analyze the power spectrum, $P_\ell(k)$, to $k_{\rm max}=0.5\,h/{\rm Mpc}$. We construct 20,000 simulated galaxy samples using our forward model, which is based on high-resolution ${\rm Q{\scriptsize UIJOTE}}$ $N$-body simulations and includes detailed survey realism for a more complete treatment of observational systematics. We then conduct SBI by training normalizing flows using the simulated samples and infer the posterior distribution of $\Lambda$CDM cosmological parameters: $\Omega_m, \Omega_b, h, n_s, \sigma_8$. We derive significant constraints on $\Omega_m$ and $\sigma_8$, which are consistent with previous works. Our constraints on $\sigma_8$ are $27\%$ more precise than standard analyses. This improvement is equivalent to the statistical gain expected from analyzing a galaxy sample that is $\sim60\%$ larger than CMASS with standard methods. It results from additional cosmological information on non-linear scales beyond the limit of current analytic models, $k > 0.25\,h/{\rm Mpc}$. While we focus on $P_\ell$ in this work for validation and comparison to the literature, ${\rm S{\scriptsize IM}BIG}$ provides a framework for analyzing galaxy clustering using any summary statistic. We expect further improvements on cosmological constraints from subsequent ${\rm S{\scriptsize IM}BIG}$ analyses of summary statistics beyond $P_\ell$.Comment: 9 pages, 5 figure

SimBIG: Field-level Simulation-Based Inference of Galaxy Clustering

We present the first simulation-based inference (SBI) of cosmological parameters from field-level analysis of galaxy clustering. Standard galaxy clustering analyses rely on analyzing summary statistics, such as the power spectrum, $P_\ell$, with analytic models based on perturbation theory. Consequently, they do not fully exploit the non-linear and non-Gaussian features of the galaxy distribution. To address these limitations, we use the {\sc SimBIG} forward modelling framework to perform SBI using normalizing flows. We apply SimBIG to a subset of the BOSS CMASS galaxy sample using a convolutional neural network with stochastic weight averaging to perform massive data compression of the galaxy field. We infer constraints on $\Omega_m = 0.267^{+0.033}_{-0.029}$ and $\sigma_8=0.762^{+0.036}_{-0.035}$. While our constraints on $\Omega_m$ are in-line with standard $P_\ell$ analyses, those on $\sigma_8$ are $2.65\times$ tighter. Our analysis also provides constraints on the Hubble constant $H_0=64.5 \pm 3.8 \ {\rm km / s / Mpc}$ from galaxy clustering alone. This higher constraining power comes from additional non-Gaussian cosmological information, inaccessible with $P_\ell$. We demonstrate the robustness of our analysis by showcasing our ability to infer unbiased cosmological constraints from a series of test simulations that are constructed using different forward models than the one used in our training dataset. This work not only presents competitive cosmological constraints but also introduces novel methods for leveraging additional cosmological information in upcoming galaxy surveys like DESI, PFS, and Euclid.Comment: 14 pages, 4 figures. A previous version of the paper was published in the ICML 2023 Workshop on Machine Learning for Astrophysic