cosmoabc: Likelihood-free inference via Population Monte Carlo Approximate Bayesian Computation

Ishida, Emille E. O.; Vitenti, Sandro D. P.; Penna-Lima, Mariana; Cisewski, Jessi; Souza, Rafael S. de; Trindade, A. M. M.; Cameron, Ewan; Busti, V. C.

doi:10.1016/j.ascom.2015.09.001

Cited by 89 publications

(102 citation statements)

References 49 publications

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“…Until now, ABC seems to already have various applications in biology-related domains (e.g., Beaumont et al 2009;Berger et al 2010;Csilléry et al 2010;Drovandi & Pettitt 2011), while applications for astronomical purposes are few: morphological transformation of galaxies (Cameron & Pettitt 2012), cosmological parameter inference using type Ia supernovae (Weyant et al 2013), constraints of the disk formation of the Milky Way (Robin et al 2014), and strong lensing properties of galaxy clusters (Killedar et al 2015). Very recently, two papers (Ishida et al 2015;Akeret et al 2015) dedicated to ABC in a general cosmological context have been submitted.…”

Section: Introductionmentioning

confidence: 99%

A new model to predict weak-lensing peak counts

Lin

Kilbinger

2015

A&A

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Context. Peak counts have been shown to be an excellent tool for extracting the non-Gaussian part of the weak lensing signal. Recently, we developed a fast stochastic forward model to predict weak-lensing peak counts. Our model is able to reconstruct the underlying distribution of observables for analysis. Aims. In this work, we explore and compare various strategies for constraining a parameter using our model, focusing on the matter density Ω m and the density fluctuation amplitude σ 8 . Methods. First, we examine the impact from the cosmological dependency of covariances (CDC). Second, we perform the analysis with the copula likelihood, a technique that makes a weaker assumption than does the Gaussian likelihood. Third, direct, non-analytic parameter estimations are applied using the full information of the distribution. Fourth, we obtain constraints with approximate Bayesian computation (ABC), an efficient, robust, and likelihood-free algorithm based on accept-reject sampling. Results. We find that neglecting the CDC effect enlarges parameter contours by 22% and that the covariance-varying copula likelihood is a very good approximation to the true likelihood. The direct techniques work well in spite of noisier contours. Concerning ABC, the iterative process converges quickly to a posterior distribution that is in excellent agreement with results from our other analyses. The time cost for ABC is reduced by two orders of magnitude. Conclusions. The stochastic nature of our weak-lensing peak count model allows us to use various techniques that approach the true underlying probability distribution of observables, without making simplifying assumptions. Our work can be generalized to other observables where forward simulations provide samples of the underlying distribution.

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Section: Introductionmentioning

confidence: 99%

A new model to predict weak-lensing peak counts

Lin

Kilbinger

2015

A&A

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“…Lin & Kilbinger (2015b) and Lin et al (2016) showed that ABC is an efficient and successful parameter inference strategy for WL peak count analyses. The method has also been used recently in several other astrophysical and cosmological applications (Cameron & Pettitt 2012;Weyant et al 2013;Robin et al 2014;Killedar et al 2015;Ishida et al 2015;Akeret et al 2015). We constrain the parameter set (Ω m , σ 8 , w We implement a population Monte Carlo (PMC) ABC algorithm to iteratively converge on the posterior distribution of parameters.…”

Section: Parameter Inference With Approximate Bayesian Computationmentioning

confidence: 99%

Cosmological constraints with weak-lensing peak counts and second-order statistics in a large-field survey

Peel

Lin

Lanusse

et al. 2017

A&A

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Peak statistics in weak-lensing maps access the non-Gaussian information contained in the large-scale distribution of matter in the Universe. They are therefore a promising complementary probe to two-point and higher-order statistics to constrain our cosmological models. Next-generation galaxy surveys, with their advanced optics and large areas, will measure the cosmic weak-lensing signal with unprecedented precision. To prepare for these anticipated data sets, we assess the constraining power of peak counts in a simulated Euclid-like survey on the cosmological parameters Ω m , σ 8 , and w de 0 . In particular, we study how Camelus, a fast stochastic model for predicting peaks, can be applied to such large surveys. The algorithm avoids the need for time-costly N-body simulations, and its stochastic approach provides full PDF information of observables. Considering peaks with a signal-to-noise ratio ≥1, we measure the abundance histogram in a mock shear catalogue of approximately 5000 deg 2 using a multiscale mass-map filtering technique. We constrain the parameters of the mock survey using Camelus combined with approximate Bayesian computation, a robust likelihoodfree inference algorithm. Peak statistics yield a tight but significantly biased constraint in the σ 8 -Ω m plane, as measured by the width ∆Σ 8 of the 1σ contour. We find Σ 8 = σ 8 (Ω m /0.27) α = 0.77−0.05 with α = 0.75 for a flat ΛCDM model. The strong bias indicates the need to better understand and control the model systematics before applying it to a real survey of this size or larger. We perform a calibration of the model and compare results to those from the two-point correlation functions ξ ± measured on the same field. We calibrate the ξ ± result as well, since its contours are also biased, although not as severely as for peaks. In this case, we find for peaks Σ 8 = 0.76 −0.01 and α = 0.70. We conclude that the constraining power can therefore be comparable between the two weak-lensing observables in large-field surveys. Furthermore, the tilt in the σ 8 -Ω m degeneracy direction for peaks with respect to that of ξ ± suggests that a combined analysis would yield tighter constraints than either measure alone. As expected, w de 0 cannot be well constrained without a tomographic analysis, but its degeneracy directions with the other two varied parameters are still clear for both peaks and ξ ± .

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“…Finally Hahn et al (2017) demonstrate the feasibility of using ABC to constrain the relationship between galaxies and their dark matter halo. The recent birth of Python packages providing sampling algorithms in an ABC framework, such as astroABC (Jennings & Madigan 2017) and ELFI (Kangasrääsiö et al 2016), which implement SMC methods, and COSMOABC (Ishida et al 2015) which implements the PMC algorithm, will probably facilitate the rise of likelihood-free inference techniques in the astronomical community.…”

Section: Introductionmentioning

confidence: 99%

Inferring the photometric and size evolution of galaxies from image simulations

Carassou

Lapparent

Bertin

et al. 2017

A&A

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Context. Current constraints on models of galaxy evolution rely on morphometric catalogs extracted from multi-band photometric surveys. However, these catalogs are altered by selection effects that are difficult to model, that correlate in non trivial ways, and that can lead to contradictory predictions if not taken into account carefully. Aims. To address this issue, we have developed a new approach combining parametric Bayesian indirect likelihood (pBIL) techniques and empirical modeling with realistic image simulations that reproduce a large fraction of these selection effects. This allows us to perform a direct comparison between observed and simulated images and to infer robust constraints on model parameters. Methods. We use a semi-empirical forward model to generate a distribution of mock galaxies from a set of physical parameters. These galaxies are passed through an image simulator reproducing the instrumental characteristics of any survey and are then extracted in the same way as the observed data. The discrepancy between the simulated and observed data is quantified, and minimized with a custom sampling process based on adaptive Markov chain Monte Carlo methods. Results. Using synthetic data matching most of the properties of a Canada-France-Hawaii Telescope Legacy Survey Deep field, we demonstrate the robustness and internal consistency of our approach by inferring the parameters governing the size and luminosity functions and their evolutions for different realistic populations of galaxies. We also compare the results of our approach with those obtained from the classical spectral energy distribution fitting and photometric redshift approach. Conclusions. Our pipeline infers efficiently the luminosity and size distribution and evolution parameters with a very limited number of observables (three photometric bands). When compared to SED fitting based on the same set of observables, our method yields results that are more accurate and free from systematic biases.

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cosmoabc: Likelihood-free inference via Population Monte Carlo Approximate Bayesian Computation

Cited by 89 publications

References 49 publications

A new model to predict weak-lensing peak counts

A new model to predict weak-lensing peak counts

Cosmological constraints with weak-lensing peak counts and second-order statistics in a large-field survey

Inferring the photometric and size evolution of galaxies from image simulations

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