Starlet higher order statistics for galaxy clustering and weak lensing

We present a first application to photometric galaxy clustering and weak lensing of wavelet based multi-scale higher order summary statistics: starlet peak counts and starlet $\ell_1$-norm. Peak counts are the local maxima in the map and the $\ell_1$-norm is computed via the sum of the absolute values of the starlet (wavelet) decomposition coefficients of a map, providing a fast multi-scale calculation of the pixel distribution, encoding the information of all pixels in the map. We employ the cosmo-SLICS simulations sources and lenses catalogues and we compute wavelet based higher order statistics in the context of combined probes and their potential when applied to the weak lensing convergence maps and galaxy maps. We get forecasts on the matter density parameter $\Omega_{\rm m}$, the reduced Hubble constant $h$, the matter fluctuation amplitude $\sigma_8$, and the dark energy equation of state parameter $w_0$. We find that, in our setting for this first application, considering the two probes as independent, starlet peaks and the $\ell_1$-norm represent interesting summary statistics that can improve the constraints with respect to the power spectrum also in the case of photometric galaxy clustering and when the two probes are combined.Comment: A&A Letters to the Editor, Forthcoming article, accepte

UNIONS: The impact of systematic errors on weak-lensing peak counts

UNIONS is an ongoing deep photometric multi-band survey of the Northern sky. As part of UNIONS, CFIS provides r-band data which we use to study weak-lensing peak counts for cosmological inference. We assess systematic effects for weak-lensing peak counts and their impact on cosmological parameters for the UNIONS survey. In particular, we present results on local calibration, metacalibration shear bias, baryonic feedback, the source galaxy redshift estimate, intrinsic alignment, and the cluster member dilution. For each uncertainty and systematic effect, we describe our mitigation scheme and the impact on cosmological parameter constraints. We obtain constraints on cosmological parameters from MCMC using CFIS data and MassiveNuS N-body simulations as a model for peak counts statistics. Depending on the calibration (local versus global, and the inclusion of the residual multiplicative shear bias), the mean matter density parameter $\Omega_m$ can shift up to $-0.024$ ($-0.5\sigma$). We also see that including baryonic corrections can shift $\Omega_m$ by $+0.027$ ($+0.5 \sigma$) with respect to the DM-only simulations. Reducing the impact of the intrinsic alignment and cluster member dilution through signal-to-noise cuts can lead to a shift in $\Omega_m$ of $+0.027$ ($+0.5 \sigma$). Finally, with a mean redshift uncertainty of $\Delta \bar{z} = 0.03$, we see that the shift of $\Omega_m$ ($+0.001$ which corresponds to $+0.02 \sigma$) is not significant. This paper investigates for the first time with UNIONS weak-lensing data and peak counts the impact of systematic effects. The value of $\Omega_m$ is the most impacted and can shift up to $\sim 0.03$ which corresponds to $0.5\sigma$ depending on the choices for each systematics. We expect constraints to become more reliable with future (larger) data catalogues, for which the current pipeline will provide a starting point.Comment: 17 pages, 17 figure

Statistiques d'ordre supérieur pour la cosmologie : développement de la fonction de vraisemblance pour des missions comme Euclid

Weak gravitational lensing by the large-scale structure is the effect of bending of light emitted by backgroundgalaxies due to the presence of foreground matter. It represents a powerful tool for estimating cosmologicalparameters, as it is sensitive to the large-scale structure of the universe. Past, present, and future cosmologicalsurveys, like the upcoming ESA Euclid mission, will use it as one of the main physical probes for investigatingunsolved questions in current cosmology, such as: what the properties of the dark components of the universeare, what the origin of its accelerated expansion is and what the sum of neutrino masses is. As weak lensingsurveys become deeper, they reveal more non-Gaussian features of the matter density field, requiring statisticsbeyond the second order to properly extract cosmological information. This has motivated the introduction ofseveral statistics of order higher than the second, such as Minkowski functionals, higher-order moments, thebispectrum, peak counts and, most recently, the scattering transform, wavelet phase harmonic statistics, andmachine learning-based methods to account for non-Gaussian information in cosmological analysis. The aim ofthis thesis is to investigate and develop statistical methods to optimally extract the information encoded in thedata in the context of higher order statistics, which can eventually help to improve the constraints oncosmological parameters in current and future cosmological analysis. In a first study, we have compared differentsummary statistics (from power spectrum to peak counts) and quantified the impact of different multi-scalefiltering techniques on cosmological forecasts obtained in an ideal setting. Specifically, we employ a starlet filter,which is a wavelet transform that enables to extract cosmological information from the maps at different scalessimultaneously. The performed study is tomographic, and we compare different summary statistics, assumingEuclid-like shape noise. The performance of the starlet is compared with the state of the art of summary statisticsin weak lensing in an ideal setting without systematics effects. The findings are that in both multi-scale settings,peak counts result to perform better than the state of the art for second order statistics and single scale peakcounts. Moreover, when using a multi-scale approach, joining power spectrum and peaks does not add anyrelevant information over considering just the peaks alone. Moreover, for the starlet filter we find that themajority of the information of the data covariance matrix is encoded in the diagonal elements. This can beadvantageous when inverting the covariance matrix, speeding up the numerical implementation. Based on thepromising performance of the multi-scale approach in the context of peak counts found in the first study, wepropose a new high order summary statistics called the starlet l1-norm. It provides a multi-scale calculation ofthe full voids and peaks distribution and avoids the problem of the definition of what is a peak and what is avoid. The outcome is that, in a tomographic ideal setting, assuming Euclid shape noise, this new summarystatistics outperforms commonly used ones, such as peak counts, minimum counts, or combination of the twoin terms of constraining power. The starlet l1-norm represents a new promising unified framework to accountfor the information encoded in peak counts and voids, preserving the advantages of the multi-scale approach.In a second part, the thesis presents preliminary results and procedures of the current work in progress. The aimis to extend the previous findings to different survey settings and cosmological probes, by applying high orderstatistics to galaxy clustering simulations for the Kilo-Degree Survey (KiDS); as the two previous works werecarried in an ideal setting, we show preliminary results of a first application to real data from the Canada-FranceImaging survey (CFIS).L’effet de lentille gravitationnelle faible lié aux structures à grande échelle est l'effet de la courbure de lalumière émise par les galaxies d'arrière-plan en raison de la présence de matière au premier plan. Il représenteun outil puissant pour estimer les paramètres cosmologiques car il est sensible aux structures à grande échellede l'univers. Les études cosmologiques passées, présentes et futures, comme la prochaine mission Euclid del'Agence spatiale européenne, l'utiliseront comme l'une des principales sondes physiques pour enquêter sur lesquestions non résolues de la cosmologie actuelle, comme les propriétés des composants sombres de l’univers,l'origine de son expansion accélérée ou de la somme totale des masses des neutrinos. Au fur et à mesure queles relevés par lentilles faibles deviennent plus profonds, ils révèlent davantage les caractéristiques nongaussiennes du champ de densité de matière, nécessitant ainsi l’utilisation de statistiques au-delà du secondordre pour mieux extraire des données les informations cosmologiques. Ceci a motivé l'introduction dedifférentes mesures statistiques d'ordre supérieur, telles que les fonctions de Minkowski, le calcul desmoments d'ordre supérieurs à 2, le bispectre, les comptages de pics des vides ou, plus récemment, lascattering transform, la décomposition wavelet phase harmonic statistics et des techniques d’intelligenceartificielle. Cette thèse étudie le potentiel d’effectuer des mesures statistiques multi-échelles pour contraindreles paramètres cosmologiques. Nous comparons d’abord deux techniques d'analyse multi-échelles sur dessimulations de cartes convergence de lentilles faibles bruitées, afin de quantifier l’impact de ce choix sur lacapacité à contraindre les paramètres. La première approche est la concaténation de filtres gaussiens suivie decomptages de pics et la seconde consiste à utiliser une transformée starlet qui est une transformée enondelettes isotrope non décimée et qui décompose une image en plusieurs bandes de même taille, permettantd'extraire simultanément des informations cosmologiques des cartes à différentes échelles. Cette étudeexploite l’information tomographique et considère un bruit d’une amplitude de l’ordre du bruit attendu avec lamission Euclid. Nous trouvons que ces deux approches de comptage de pics multi-échelles surpassent les plusméthodes couramment utilisées qui sont les statistiques de second ordre comme le spectre de puissance ou lecomptage de pics à une seule échelle.De plus, nous observons que dans le cas d’une analyse multi-échelle, combiner les pics multi-échelles avec lespectre de puissance n'ajoute aucune information supplémentaire par rapport à la prise en compteuniquement des pics. L’avantage de la transformée starlet par rapport aux filtres gaussiens est que la matricede covariance est quasiment diagonale, ce qui facilite son inversion. Nous proposons ensuite de remplacer lecomptage de pic multi-échelle par un nouveau descripteur statistique, que nous appelons l1-norm starlet, etqui consiste à sommer la norme l1 des coefficients starlets de la carte de convergence. Ceci évite de devoirdéfinir la notion de pic ou de vide, et permet de tenir compte de toute l’information contenu dans lescoefficients dans notre analyse. Outre le fait d’élégamment unifier l’analyse des pics et des vides, cettenouvelle méthodologie est plus efficace non seulement que chacune des deux indépendamment mais aussi del’analyse jointe pics-vides. Dans la suite, nous montrons des résultats préliminaires relatif à l’application denotre nouvelle méthodologie pour le relevé de galaxies KiDS (Kilo-Degree Survey) et également pour une autresonde, le clustering des galaxies. Nous étudions aussi la robustesse de notre approche sur les données réellesdu relevé Canada-France Imagerie (CFIS)

Statistiques d'ordre supérieur pour la cosmologie : développement de la fonction de vraisemblance pour des missions comme Euclid

Weak gravitational lensing by the large-scale structure is the effect of bending of light emitted by backgroundgalaxies due to the presence of foreground matter. It represents a powerful tool for estimating cosmologicalparameters, as it is sensitive to the large-scale structure of the universe. Past, present, and future cosmologicalsurveys, like the upcoming ESA Euclid mission, will use it as one of the main physical probes for investigatingunsolved questions in current cosmology, such as: what the properties of the dark components of the universeare, what the origin of its accelerated expansion is and what the sum of neutrino masses is. As weak lensingsurveys become deeper, they reveal more non-Gaussian features of the matter density field, requiring statisticsbeyond the second order to properly extract cosmological information. This has motivated the introduction ofseveral statistics of order higher than the second, such as Minkowski functionals, higher-order moments, thebispectrum, peak counts and, most recently, the scattering transform, wavelet phase harmonic statistics, andmachine learning-based methods to account for non-Gaussian information in cosmological analysis. The aim ofthis thesis is to investigate and develop statistical methods to optimally extract the information encoded in thedata in the context of higher order statistics, which can eventually help to improve the constraints oncosmological parameters in current and future cosmological analysis. In a first study, we have compared differentsummary statistics (from power spectrum to peak counts) and quantified the impact of different multi-scalefiltering techniques on cosmological forecasts obtained in an ideal setting. Specifically, we employ a starlet filter,which is a wavelet transform that enables to extract cosmological information from the maps at different scalessimultaneously. The performed study is tomographic, and we compare different summary statistics, assumingEuclid-like shape noise. The performance of the starlet is compared with the state of the art of summary statisticsin weak lensing in an ideal setting without systematics effects. The findings are that in both multi-scale settings,peak counts result to perform better than the state of the art for second order statistics and single scale peakcounts. Moreover, when using a multi-scale approach, joining power spectrum and peaks does not add anyrelevant information over considering just the peaks alone. Moreover, for the starlet filter we find that themajority of the information of the data covariance matrix is encoded in the diagonal elements. This can beadvantageous when inverting the covariance matrix, speeding up the numerical implementation. Based on thepromising performance of the multi-scale approach in the context of peak counts found in the first study, wepropose a new high order summary statistics called the starlet l1-norm. It provides a multi-scale calculation ofthe full voids and peaks distribution and avoids the problem of the definition of what is a peak and what is avoid. The outcome is that, in a tomographic ideal setting, assuming Euclid shape noise, this new summarystatistics outperforms commonly used ones, such as peak counts, minimum counts, or combination of the twoin terms of constraining power. The starlet l1-norm represents a new promising unified framework to accountfor the information encoded in peak counts and voids, preserving the advantages of the multi-scale approach.In a second part, the thesis presents preliminary results and procedures of the current work in progress. The aimis to extend the previous findings to different survey settings and cosmological probes, by applying high orderstatistics to galaxy clustering simulations for the Kilo-Degree Survey (KiDS); as the two previous works werecarried in an ideal setting, we show preliminary results of a first application to real data from the Canada-FranceImaging survey (CFIS).L’effet de lentille gravitationnelle faible lié aux structures à grande échelle est l'effet de la courbure de lalumière émise par les galaxies d'arrière-plan en raison de la présence de matière au premier plan. Il représenteun outil puissant pour estimer les paramètres cosmologiques car il est sensible aux structures à grande échellede l'univers. Les études cosmologiques passées, présentes et futures, comme la prochaine mission Euclid del'Agence spatiale européenne, l'utiliseront comme l'une des principales sondes physiques pour enquêter sur lesquestions non résolues de la cosmologie actuelle, comme les propriétés des composants sombres de l’univers,l'origine de son expansion accélérée ou de la somme totale des masses des neutrinos. Au fur et à mesure queles relevés par lentilles faibles deviennent plus profonds, ils révèlent davantage les caractéristiques nongaussiennes du champ de densité de matière, nécessitant ainsi l’utilisation de statistiques au-delà du secondordre pour mieux extraire des données les informations cosmologiques. Ceci a motivé l'introduction dedifférentes mesures statistiques d'ordre supérieur, telles que les fonctions de Minkowski, le calcul desmoments d'ordre supérieurs à 2, le bispectre, les comptages de pics des vides ou, plus récemment, lascattering transform, la décomposition wavelet phase harmonic statistics et des techniques d’intelligenceartificielle. Cette thèse étudie le potentiel d’effectuer des mesures statistiques multi-échelles pour contraindreles paramètres cosmologiques. Nous comparons d’abord deux techniques d'analyse multi-échelles sur dessimulations de cartes convergence de lentilles faibles bruitées, afin de quantifier l’impact de ce choix sur lacapacité à contraindre les paramètres. La première approche est la concaténation de filtres gaussiens suivie decomptages de pics et la seconde consiste à utiliser une transformée starlet qui est une transformée enondelettes isotrope non décimée et qui décompose une image en plusieurs bandes de même taille, permettantd'extraire simultanément des informations cosmologiques des cartes à différentes échelles. Cette étudeexploite l’information tomographique et considère un bruit d’une amplitude de l’ordre du bruit attendu avec lamission Euclid. Nous trouvons que ces deux approches de comptage de pics multi-échelles surpassent les plusméthodes couramment utilisées qui sont les statistiques de second ordre comme le spectre de puissance ou lecomptage de pics à une seule échelle.De plus, nous observons que dans le cas d’une analyse multi-échelle, combiner les pics multi-échelles avec lespectre de puissance n'ajoute aucune information supplémentaire par rapport à la prise en compteuniquement des pics. L’avantage de la transformée starlet par rapport aux filtres gaussiens est que la matricede covariance est quasiment diagonale, ce qui facilite son inversion. Nous proposons ensuite de remplacer lecomptage de pic multi-échelle par un nouveau descripteur statistique, que nous appelons l1-norm starlet, etqui consiste à sommer la norme l1 des coefficients starlets de la carte de convergence. Ceci évite de devoirdéfinir la notion de pic ou de vide, et permet de tenir compte de toute l’information contenu dans lescoefficients dans notre analyse. Outre le fait d’élégamment unifier l’analyse des pics et des vides, cettenouvelle méthodologie est plus efficace non seulement que chacune des deux indépendamment mais aussi del’analyse jointe pics-vides. Dans la suite, nous montrons des résultats préliminaires relatif à l’application denotre nouvelle méthodologie pour le relevé de galaxies KiDS (Kilo-Degree Survey) et également pour une autresonde, le clustering des galaxies. Nous étudions aussi la robustesse de notre approche sur les données réellesdu relevé Canada-France Imagerie (CFIS)

Statistiques d'ordre supérieur pour la cosmologie : développement de la fonction de vraisemblance pour des missions comme Euclid

L’effet de lentille gravitationnelle faible lié aux structures à grande échelle est l'effet de la courbure de lalumière émise par les galaxies d'arrière-plan en raison de la présence de matière au premier plan. Il représenteun outil puissant pour estimer les paramètres cosmologiques car il est sensible aux structures à grande échellede l'univers. Les études cosmologiques passées, présentes et futures, comme la prochaine mission Euclid del'Agence spatiale européenne, l'utiliseront comme l'une des principales sondes physiques pour enquêter sur lesquestions non résolues de la cosmologie actuelle, comme les propriétés des composants sombres de l’univers,l'origine de son expansion accélérée ou de la somme totale des masses des neutrinos. Au fur et à mesure queles relevés par lentilles faibles deviennent plus profonds, ils révèlent davantage les caractéristiques nongaussiennes du champ de densité de matière, nécessitant ainsi l’utilisation de statistiques au-delà du secondordre pour mieux extraire des données les informations cosmologiques. Ceci a motivé l'introduction dedifférentes mesures statistiques d'ordre supérieur, telles que les fonctions de Minkowski, le calcul desmoments d'ordre supérieurs à 2, le bispectre, les comptages de pics des vides ou, plus récemment, lascattering transform, la décomposition wavelet phase harmonic statistics et des techniques d’intelligenceartificielle. Cette thèse étudie le potentiel d’effectuer des mesures statistiques multi-échelles pour contraindreles paramètres cosmologiques. Nous comparons d’abord deux techniques d'analyse multi-échelles sur dessimulations de cartes convergence de lentilles faibles bruitées, afin de quantifier l’impact de ce choix sur lacapacité à contraindre les paramètres. La première approche est la concaténation de filtres gaussiens suivie decomptages de pics et la seconde consiste à utiliser une transformée starlet qui est une transformée enondelettes isotrope non décimée et qui décompose une image en plusieurs bandes de même taille, permettantd'extraire simultanément des informations cosmologiques des cartes à différentes échelles. Cette étudeexploite l’information tomographique et considère un bruit d’une amplitude de l’ordre du bruit attendu avec lamission Euclid. Nous trouvons que ces deux approches de comptage de pics multi-échelles surpassent les plusméthodes couramment utilisées qui sont les statistiques de second ordre comme le spectre de puissance ou lecomptage de pics à une seule échelle.De plus, nous observons que dans le cas d’une analyse multi-échelle, combiner les pics multi-échelles avec lespectre de puissance n'ajoute aucune information supplémentaire par rapport à la prise en compteuniquement des pics. L’avantage de la transformée starlet par rapport aux filtres gaussiens est que la matricede covariance est quasiment diagonale, ce qui facilite son inversion. Nous proposons ensuite de remplacer lecomptage de pic multi-échelle par un nouveau descripteur statistique, que nous appelons l1-norm starlet, etqui consiste à sommer la norme l1 des coefficients starlets de la carte de convergence. Ceci évite de devoirdéfinir la notion de pic ou de vide, et permet de tenir compte de toute l’information contenu dans lescoefficients dans notre analyse. Outre le fait d’élégamment unifier l’analyse des pics et des vides, cettenouvelle méthodologie est plus efficace non seulement que chacune des deux indépendamment mais aussi del’analyse jointe pics-vides. Dans la suite, nous montrons des résultats préliminaires relatif à l’application denotre nouvelle méthodologie pour le relevé de galaxies KiDS (Kilo-Degree Survey) et également pour une autresonde, le clustering des galaxies. Nous étudions aussi la robustesse de notre approche sur les données réellesdu relevé Canada-France Imagerie (CFIS).Weak gravitational lensing by the large-scale structure is the effect of bending of light emitted by backgroundgalaxies due to the presence of foreground matter. It represents a powerful tool for estimating cosmologicalparameters, as it is sensitive to the large-scale structure of the universe. Past, present, and future cosmologicalsurveys, like the upcoming ESA Euclid mission, will use it as one of the main physical probes for investigatingunsolved questions in current cosmology, such as: what the properties of the dark components of the universeare, what the origin of its accelerated expansion is and what the sum of neutrino masses is. As weak lensingsurveys become deeper, they reveal more non-Gaussian features of the matter density field, requiring statisticsbeyond the second order to properly extract cosmological information. This has motivated the introduction ofseveral statistics of order higher than the second, such as Minkowski functionals, higher-order moments, thebispectrum, peak counts and, most recently, the scattering transform, wavelet phase harmonic statistics, andmachine learning-based methods to account for non-Gaussian information in cosmological analysis. The aim ofthis thesis is to investigate and develop statistical methods to optimally extract the information encoded in thedata in the context of higher order statistics, which can eventually help to improve the constraints oncosmological parameters in current and future cosmological analysis. In a first study, we have compared differentsummary statistics (from power spectrum to peak counts) and quantified the impact of different multi-scalefiltering techniques on cosmological forecasts obtained in an ideal setting. Specifically, we employ a starlet filter,which is a wavelet transform that enables to extract cosmological information from the maps at different scalessimultaneously. The performed study is tomographic, and we compare different summary statistics, assumingEuclid-like shape noise. The performance of the starlet is compared with the state of the art of summary statisticsin weak lensing in an ideal setting without systematics effects. The findings are that in both multi-scale settings,peak counts result to perform better than the state of the art for second order statistics and single scale peakcounts. Moreover, when using a multi-scale approach, joining power spectrum and peaks does not add anyrelevant information over considering just the peaks alone. Moreover, for the starlet filter we find that themajority of the information of the data covariance matrix is encoded in the diagonal elements. This can beadvantageous when inverting the covariance matrix, speeding up the numerical implementation. Based on thepromising performance of the multi-scale approach in the context of peak counts found in the first study, wepropose a new high order summary statistics called the starlet l1-norm. It provides a multi-scale calculation ofthe full voids and peaks distribution and avoids the problem of the definition of what is a peak and what is avoid. The outcome is that, in a tomographic ideal setting, assuming Euclid shape noise, this new summarystatistics outperforms commonly used ones, such as peak counts, minimum counts, or combination of the twoin terms of constraining power. The starlet l1-norm represents a new promising unified framework to accountfor the information encoded in peak counts and voids, preserving the advantages of the multi-scale approach.In a second part, the thesis presents preliminary results and procedures of the current work in progress. The aimis to extend the previous findings to different survey settings and cosmological probes, by applying high orderstatistics to galaxy clustering simulations for the Kilo-Degree Survey (KiDS); as the two previous works werecarried in an ideal setting, we show preliminary results of a first application to real data from the Canada-FranceImaging survey (CFIS)

Statistiques d'ordre supérieur pour la cosmologie : développement de la fonction de vraisemblance pour des missions comme Euclid

Weak gravitational lensing by the large-scale structure is the effect of bending of light emitted by backgroundgalaxies due to the presence of foreground matter. It represents a powerful tool for estimating cosmologicalparameters, as it is sensitive to the large-scale structure of the universe. Past, present, and future cosmologicalsurveys, like the upcoming ESA Euclid mission, will use it as one of the main physical probes for investigatingunsolved questions in current cosmology, such as: what the properties of the dark components of the universeare, what the origin of its accelerated expansion is and what the sum of neutrino masses is. As weak lensingsurveys become deeper, they reveal more non-Gaussian features of the matter density field, requiring statisticsbeyond the second order to properly extract cosmological information. This has motivated the introduction ofseveral statistics of order higher than the second, such as Minkowski functionals, higher-order moments, thebispectrum, peak counts and, most recently, the scattering transform, wavelet phase harmonic statistics, andmachine learning-based methods to account for non-Gaussian information in cosmological analysis. The aim ofthis thesis is to investigate and develop statistical methods to optimally extract the information encoded in thedata in the context of higher order statistics, which can eventually help to improve the constraints oncosmological parameters in current and future cosmological analysis. In a first study, we have compared differentsummary statistics (from power spectrum to peak counts) and quantified the impact of different multi-scalefiltering techniques on cosmological forecasts obtained in an ideal setting. Specifically, we employ a starlet filter,which is a wavelet transform that enables to extract cosmological information from the maps at different scalessimultaneously. The performed study is tomographic, and we compare different summary statistics, assumingEuclid-like shape noise. The performance of the starlet is compared with the state of the art of summary statisticsin weak lensing in an ideal setting without systematics effects. The findings are that in both multi-scale settings,peak counts result to perform better than the state of the art for second order statistics and single scale peakcounts. Moreover, when using a multi-scale approach, joining power spectrum and peaks does not add anyrelevant information over considering just the peaks alone. Moreover, for the starlet filter we find that themajority of the information of the data covariance matrix is encoded in the diagonal elements. This can beadvantageous when inverting the covariance matrix, speeding up the numerical implementation. Based on thepromising performance of the multi-scale approach in the context of peak counts found in the first study, wepropose a new high order summary statistics called the starlet l1-norm. It provides a multi-scale calculation ofthe full voids and peaks distribution and avoids the problem of the definition of what is a peak and what is avoid. The outcome is that, in a tomographic ideal setting, assuming Euclid shape noise, this new summarystatistics outperforms commonly used ones, such as peak counts, minimum counts, or combination of the twoin terms of constraining power. The starlet l1-norm represents a new promising unified framework to accountfor the information encoded in peak counts and voids, preserving the advantages of the multi-scale approach.In a second part, the thesis presents preliminary results and procedures of the current work in progress. The aimis to extend the previous findings to different survey settings and cosmological probes, by applying high orderstatistics to galaxy clustering simulations for the Kilo-Degree Survey (KiDS); as the two previous works werecarried in an ideal setting, we show preliminary results of a first application to real data from the Canada-FranceImaging survey (CFIS).L’effet de lentille gravitationnelle faible lié aux structures à grande échelle est l'effet de la courbure de lalumière émise par les galaxies d'arrière-plan en raison de la présence de matière au premier plan. Il représenteun outil puissant pour estimer les paramètres cosmologiques car il est sensible aux structures à grande échellede l'univers. Les études cosmologiques passées, présentes et futures, comme la prochaine mission Euclid del'Agence spatiale européenne, l'utiliseront comme l'une des principales sondes physiques pour enquêter sur lesquestions non résolues de la cosmologie actuelle, comme les propriétés des composants sombres de l’univers,l'origine de son expansion accélérée ou de la somme totale des masses des neutrinos. Au fur et à mesure queles relevés par lentilles faibles deviennent plus profonds, ils révèlent davantage les caractéristiques nongaussiennes du champ de densité de matière, nécessitant ainsi l’utilisation de statistiques au-delà du secondordre pour mieux extraire des données les informations cosmologiques. Ceci a motivé l'introduction dedifférentes mesures statistiques d'ordre supérieur, telles que les fonctions de Minkowski, le calcul desmoments d'ordre supérieurs à 2, le bispectre, les comptages de pics des vides ou, plus récemment, lascattering transform, la décomposition wavelet phase harmonic statistics et des techniques d’intelligenceartificielle. Cette thèse étudie le potentiel d’effectuer des mesures statistiques multi-échelles pour contraindreles paramètres cosmologiques. Nous comparons d’abord deux techniques d'analyse multi-échelles sur dessimulations de cartes convergence de lentilles faibles bruitées, afin de quantifier l’impact de ce choix sur lacapacité à contraindre les paramètres. La première approche est la concaténation de filtres gaussiens suivie decomptages de pics et la seconde consiste à utiliser une transformée starlet qui est une transformée enondelettes isotrope non décimée et qui décompose une image en plusieurs bandes de même taille, permettantd'extraire simultanément des informations cosmologiques des cartes à différentes échelles. Cette étudeexploite l’information tomographique et considère un bruit d’une amplitude de l’ordre du bruit attendu avec lamission Euclid. Nous trouvons que ces deux approches de comptage de pics multi-échelles surpassent les plusméthodes couramment utilisées qui sont les statistiques de second ordre comme le spectre de puissance ou lecomptage de pics à une seule échelle.De plus, nous observons que dans le cas d’une analyse multi-échelle, combiner les pics multi-échelles avec lespectre de puissance n'ajoute aucune information supplémentaire par rapport à la prise en compteuniquement des pics. L’avantage de la transformée starlet par rapport aux filtres gaussiens est que la matricede covariance est quasiment diagonale, ce qui facilite son inversion. Nous proposons ensuite de remplacer lecomptage de pic multi-échelle par un nouveau descripteur statistique, que nous appelons l1-norm starlet, etqui consiste à sommer la norme l1 des coefficients starlets de la carte de convergence. Ceci évite de devoirdéfinir la notion de pic ou de vide, et permet de tenir compte de toute l’information contenu dans lescoefficients dans notre analyse. Outre le fait d’élégamment unifier l’analyse des pics et des vides, cettenouvelle méthodologie est plus efficace non seulement que chacune des deux indépendamment mais aussi del’analyse jointe pics-vides. Dans la suite, nous montrons des résultats préliminaires relatif à l’application denotre nouvelle méthodologie pour le relevé de galaxies KiDS (Kilo-Degree Survey) et également pour une autresonde, le clustering des galaxies. Nous étudions aussi la robustesse de notre approche sur les données réellesdu relevé Canada-France Imagerie (CFIS)

Euclid preparation: XXVIII. Forecasts for ten different higher-order weak lensing statistics

Recent cosmic shear studies have shown that higher-order statistics (HOS) developed by independent teams now outperform standard two-point estimators in terms of statistical precision thanks to their sensitivity to the non-Gaussian features of large-scale structure. The aim of the Higher-Order Weak Lensing Statistics (HOWLS) project is to assess, compare, and combine the constraining power of ten different HOS on a common set of Euclid-like mocks, derived from N-body simulations. In this first paper of the HOWLS series, we computed the nontomographic (Ωm, σ8) Fisher information for the one-point probability distribution function, peak counts, Minkowski functionals, Betti numbers, persistent homology Betti numbers and heatmap, and scattering transform coefficients, and we compare them to the shear and convergence two-point correlation functions in the absence of any systematic bias. We also include forecasts for three implementations of higher-order moments, but these cannot be robustly interpreted as the Gaussian likelihood assumption breaks down for these statistics. Taken individually, we find that each HOS outperforms the two-point statistics by a factor of around two in the precision of the forecasts with some variations across statistics and cosmological parameters. When combining all the HOS, this increases to a 4.5 times improvement, highlighting the immense potential of HOS for cosmic shear cosmological analyses with Euclid. The data used in this analysis are publicly released with the paper.ISSN:0004-6361ISSN:1432-074

Starlet ℓ1-norm for weak lensing cosmology

International audienceWe present a new summary statistic for weak lensing observables, higher than second order, suitable for extracting non-Gaussian cosmological information and inferring cosmological parameters. We name this statistic the ‘starlet ℓ1-norm’ as it is computed via the sum of the absolute values of the starlet (wavelet) decomposition coefficients of a weak lensing map. In comparison to the state-of-the-art higher-order statistics – weak lensing peak counts and minimum counts, or the combination of the two – the ℓ1-norm provides a fast multi-scale calculation of the full void and peak distribution, avoiding the problem of defining what a peak is and what a void is: the ℓ1-norm carries the information encoded in all pixels of the map, not just the ones in local maxima and minima. We show its potential by applying it to the weak lensing convergence maps provided by the MassiveNus simulations to get constraints on the sum of neutrino masses, the matter density parameter, and the amplitude of the primordial power spectrum. We find that, in an ideal setting without further systematics, the starlet ℓ1-norm remarkably outperforms commonly used summary statistics, such as the power spectrum or the combination of peak and void counts, in terms of constraining power, representing a promising new unified framework to simultaneously account for the information encoded in peak counts and voids. We find that the starlet ℓ1-norm outperforms the power spectrum by 72% on Mν, 60% on Ωm, and 75% on As for the Euclid-like setting considered; it also improves upon the state-of-the-art combination of peaks and voids for a single smoothing scale by 24% on Mν, 50% on Ωm, and 24% on As

Starlet higher order statistics for galaxy clustering and weak lensing

International audienceWe present a first application to photometric galaxy clustering and weak lensing of wavelet based multi-scale higher order summary statistics: starlet peak counts and starlet $\ell_1$-norm. Peak counts are the local maxima in the map and the $\ell_1$-norm is computed via the sum of the absolute values of the starlet (wavelet) decomposition coefficients of a map, providing a fast multi-scale calculation of the pixel distribution, encoding the information of all pixels in the map. We employ the cosmo-SLICS simulations sources and lenses catalogues and we compute wavelet based higher order statistics in the context of combined probes and their potential when applied to the weak lensing convergence maps and galaxy maps. We get forecasts on the matter density parameter $\Omega_{\rm m}$, the reduced Hubble constant $h$, the matter fluctuation amplitude $\sigma_8$, and the dark energy equation of state parameter $w_0$. We find that, in our setting for this first application, considering the two probes as independent, starlet peaks and the $\ell_1$-norm represent interesting summary statistics that can improve the constraints with respect to the power spectrum also in the case of photometric galaxy clustering and when the two probes are combined

Starlet higher order statistics for galaxy clustering and weak lensing

We present a first application to photometric galaxy clustering and weak lensing of wavelet-based multi-scale (beyond two points) summary statistics: starlet peak counts and starletl1-norm. Peak counts are the local maxima in the map, andl1-norm is computed via the sum of the absolute values of the starlet (wavelet) decomposition coefficients of a map, providing a fast multi-scale calculation of the pixel distribution, encoding the information of all pixels in the map. We employ the cosmo-SLICS simulations sources and lens catalogues, and we compute wavelet-based non-Gaussian statistics in the context of combined probes and their potential when applied to the weak-lensing convergence maps and galaxy maps. We obtain forecasts on the matter density parameter Ωm, the reduced Hubble constant h, the matter fluctuation amplitude σ8, and the dark energy equation of state parameter w0. In our setting for this first application, we consider the two probes to be independent. We find that the starlet peaks and thel1-norm represent interesting summary statistics that can improve the constraints with respect to the power spectrum, even in the case of photometric galaxy clustering and when the two probes are combined.ISSN:0004-6361ISSN:1432-074