Primordial power spectrum and cosmology from black-box galaxy surveys

Leclercq, Florent; Enzi, Wolfgang; Jasche, Jens; Heavens, Alan

doi:10.1093/mnras/stz2718

Cited by 22 publications

(17 citation statements)

References 61 publications

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“…Jennings & Madigan 2017;Herbel et al 2017;Hahn et al 2017;List & Lewis 2020;Leclercq et al 2019;Alsing et al 2019; Kacprzak et al 2 In the rest of this paper, we will follow recent convention and use the term SBI.MNRAS 000,1-19 (2021) …”

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confidence: 99%

Accurate X-ray Timing in the Presence of Systematic Biases With Simulation-Based Inference

Huppenkothen,

Bachetti

2021

Preprint

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Because many of our X-ray telescopes are optimized towards observing faint sources, observations of bright sources like X-ray binaries in outburst are often affected by instrumental biases. These effects include dead time and photon pile-up, which can dramatically change the statistical inference of physical parameters from these observations. While dead time is difficult to take into account in a statistically consistent manner, simulating dead time-affected data is often straightforward. This structure makes the issue of inferring physical properties from dead time-affected observations fall into a class of problems common across many scientific disciplines. There is a growing number of methods to address them under the names of Approximate Bayesian Computation (ABC) or Simulation-Based Inference (SBI), aided by new developments in density estimation and statistical machine learning. In this paper, we introduce SBI as a principled way to infer variability properties from dead time-affected light curves. We use Sequential Neural Posterior Estimation to estimate the posterior probability for variability properties. We show that this method can recover variability parameters on simulated data even when dead time is variable, and present results of an application of this approach to NuSTAR observations of the galactic black hole X-ray binary GRS 1915+105.

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confidence: 99%

Accurate X-ray Timing in the Presence of Systematic Biases With Simulation-Based Inference

Huppenkothen,

Bachetti

2021

Preprint

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“…Moreover, if we want to use a more sophisticated sampler such as Hamiltonian Monte Carlo (HMC), one can leverage the gradients from the emulator to derive an expression for the gradient of the negative loglikelihood (the potential energy function in an HMC scheme) with respect to the input cosmological parameters, under the assumption that such an analytic derivation is possible. Furthermore, the second derivatives can be used in a Fisher Matrix analysis, or the first and second derivatives can be be used together in an approximate inference scheme based on Taylor expansion techniques, see for example, the recent work by Leclercq et al (2019). In addition, similar concepts behind this work can be extended to build emulators for P δ (k, z) from Nbody simulations.…”

Section: Discussionmentioning

confidence: 99%

Kernel-Based Emulator for the 3D Matter Power Spectrum from CLASS

Mootoovaloo,

Jaffe,

Heavens

et al. 2021

Preprint

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The 3D matter power spectrum, P δ (k, z) is a fundamental quantity in the analysis of cosmological data such as large-scale structure, 21cm observations, and weak lensing. Existing computer models (Boltzmann codes) such as CLASS can provide it at the expense of immoderate computational cost. In this paper, we propose a fast Bayesian method to generate the 3D matter power spectrum, for a given set of wavenumbers, k and redshifts, z. Our code allows one to calculate the following quantities: the linear matter power spectrum at a given redshift (the default is set to 0); the non-linear 3D matter power spectrum with/without baryon feedback; the weak lensing power spectrum. The gradient of the 3D matter power spectrum with respect to the input cosmological parameters is also returned and this is useful for Hamiltonian Monte Carlo samplers. The derivatives are also useful for Fisher matrix calculations. In our application, the emulator is accurate when evaluated at a set of cosmological parameters, drawn from the prior, with the fractional uncertainty, ∆P δ /P δ centered on 0. It is also ∼ 300 times faster compared to CLASS, hence making the emulator amenable to sampling cosmological and nuisance parameters in a Monte Carlo routine. In addition, once the 3D matter power spectrum is calculated, it can be used with a specific redshift distribution, n(z) to calculate the weak lensing and intrinsic alignment power spectra, which can then be used to derive constraints on cosmological parameters in a weak lensing data analysis problem. The software (emuPK) can be trained with any set of points and is distributed on Github, and comes with with a pre-trained set of Gaussian Process (GP) models, based on 1000 Latin Hypercube (LH) samples, which follow roughly the current priors for current weak lensing analyses.

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“…In the same spectrum, Alsing et al (2018) developed a density-estimation likelihood-free method and argued that it requires less tuning compared to traditional approaches such as Approximate Bayesian Computation, ABC. Leclercq et al (2019) also developed a likelihood-free approach to infer power spectrum and cosmological parameters from forward simulations only.…”

Section: Introductionmentioning

confidence: 99%

Parameter inference for weak lensing using Gaussian Processes and MOPED

Mootoovaloo

Heavens

Jaffe

et al. 2020

Monthly Notices of the Royal Astronomical Society

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In this paper, we propose a Gaussian Process (GP) emulator for the calculation both of tomographic weak lensing band-powers, and of coefficients of summary data massively compressed with the MOPED algorithm. In the former case cosmological parameter inference is accelerated by a factor of ∼10-30 compared with Boltzmann solver CLASS applied to KiDS-450 weak lensing data. Much larger gains of order 103 will come with future data, and MOPED with GPs will be fast enough to permit the Limber approximation to be dropped, with acceleration in this case of ∼105. A potential advantage of GPs is that an error on the emulated function can be computed and this uncertainty incorporated into the likelihood. However, it is known that the GP error can be unreliable when applied to deterministic functions, and we find, using the Kullback-Leibler divergence between the emulator and CLASS likelihoods, and from the uncertainties on the parameters, that agreement is better when the GP uncertainty is not used. In future, weak lensing surveys such as Euclid, and the Legacy Survey of Space and Time (LSST), will have up to ∼104 summary statistics, and inference will be correspondingly more challenging. However, since the speed of MOPED is determined not the number of summary data, but by the number of parameters, MOPED analysis scales almost perfectly, provided that a fast way to compute the theoretical MOPED coefficients is available. The GP provides such a fast mechanism.

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Primordial power spectrum and cosmology from black-box galaxy surveys

Cited by 22 publications

References 61 publications

Accurate X-ray Timing in the Presence of Systematic Biases With Simulation-Based Inference

Accurate X-ray Timing in the Presence of Systematic Biases With Simulation-Based Inference

Kernel-Based Emulator for the 3D Matter Power Spectrum from CLASS

Parameter inference for weak lensing using Gaussian Processes and MOPED

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