Cobaya: code for Bayesian analysis of hierarchical physical models

Torrado, Jesús; Lewis, Antony

doi:10.1088/1475-7516/2021/05/057

Cited by 360 publications

(202 citation statements)

References 43 publications

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“…We thank Lennart Balkenhol, Neil Goeckner-Wald, Chao-Lin Kuo, Clem Pryke, Bryan Steinbach and Matthieu Tristram for many stimulating comments. The results in this paper have been derived using numpy (Harris et al 2020), scipy (Virtanen et al 2020), NaMaster (Alonso et al 2019), the cobaya framework (Torrado & Lewis 2021), the LoLLiPoP likelihood (Mangilli et al 2015;Tristram et al 2020) as well as the HEALPix 3 and healpy packages (Gorski et al 2005;Zonca et al 2019)…”

Section: Acknowledgementsmentioning

confidence: 99%

Bias on Tensor-to-Scalar Ratio Inference With Estimated Covariance Matrices

Beck,

Cukierman,

2022

Preprint

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We investigate simulation-based bandpower covariance matrices commonly used in cosmological parameter inferences such as the estimation of the tensor-to-scalar ratio 𝑟. We find that upper limits on 𝑟 can be biased low. The underestimation of the upper limit is most severe when the number of simulation realizations is similar to the number of observables. Convergence of the covariance-matrix estimation can require a number of simulations an order of magnitude larger than the number of observables. This is found to be caused by an additional scatter in the posterior probability of 𝑟 due to Monte Carlo noise in the estimated bandpower covariance matrix, in particular, by spurious non-zero off-diagonal elements. We show that matrix conditioning can be a viable mitigation strategy in the case that legitimate covariance assumptions can be made.

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Section: Acknowledgementsmentioning

confidence: 99%

Bias on Tensor-to-Scalar Ratio Inference With Estimated Covariance Matrices

Beck,

Cukierman,

2022

Preprint

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“…We assume our correlation function measurements are drawn from a multivariate Gaussian distribution, and use uniform priors for all model parameters, given in Table 1. We explore the posterior surface for the fit between data and the correlation function predictions using a Markov-Chain Monte-Carlo (MCMC) sampler within the Cobaya 2 framework (Torrado & Lewis 2021). We include the full A HOD parameter space in our fit, however we limit the wCDM cosmological parameter space by fixing 𝑁 eff = 3.046 2 Cobaya, a code for bayesian analysis in cosmology, is the Python successor to CosmoMC.…”

Section: Exploring the Likelihoodmentioning

confidence: 99%

The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: measurement of the growth rate of structure from the small-scale clustering of the luminous red galaxy sample

Chapman¹,

Mohammad²,

Zhai³

et al. 2021

Preprint

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We measure the small-scale clustering of the Data Release 16 extended Baryon Oscillation Spectroscopic Survey Luminous Red Galaxy sample, corrected for fibre-collisions using Pairwise Inverse Probability weights, which give unbiased clustering measurements on all scales. We fit to the monopole and quadrupole moments and to the projected correlation function over the separation range 7 − 60 ℎ −1 Mpc with a model based on the cosmological emulator to measure the growth rate of cosmic structure, parameterized by 𝑓 𝜎 8 . We obtain a measurement of 𝑓 𝜎 8 (𝑧 = 0.737) = 0.408 ± 0.038, which is 1.4𝜎 lower than the value expected from 2018 Planck data for a flat ΛCDM model, and is more consistent with recent weak-lensing measurements. The level of precision achieved is 1.7 times better than more standard measurements made using only the large-scale modes of the same sample. We also fit to the data using the full range of scales 0.1 − 60 ℎ −1 Mpc modelled by the cosmological emulator and find a 4.5𝜎 tension in the amplitude of the halo velocity field with the Planck+ΛCDM model, driven by a mismatch on the non-linear scales. This may not be cosmological in origin, and could be due to a breakdown in the Halo Occupation Distribution model used in the emulator. Finally, we perform a robust analysis of possible sources of systematics, including the effects of redshift uncertainty and incompleteness due to target selection that were not included in previous analyses fitting to clustering measurements on small scales.

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“…We investigate the statistics in the full 6-dimensional parameter space for a subset of 100 of the N real = 30, σmap = 10 µK-arcmin simulations. We use Cobaya (Torrado & Lewis 2021) to find the minimum of the likelihood for these realisations. Since the simulated surveys lack access to information from large angular scales, we fix the optical depth to reionisation τ to the input value.…”

Section: Impact On Cosmological Parametersmentioning

confidence: 99%

The Parameter-Level Performance of Covariance Matrix Conditioning in Cosmic Microwave Background Data Analyses

Balkenhol,

Reichardt

2021

Preprint

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Empirical estimates of the band power covariance matrix are commonly used in cosmic microwave background (CMB) power spectrum analyses. While this approach easily captures correlations in the data, noise in the resulting covariance estimate can systematically bias the parameter fitting. Conditioning the estimated covariance matrix, by applying prior information on the shape of the eigenvectors, can reduce these biases and ensure the recovery of robust parameter constraints. In this work, we use simulations to benchmark the performance of four different conditioning schemes, motivated by contemporary CMB analyses. The simulated surveys measure the T T , TE, and EE power spectra over the angular multipole range 300 ≤ ≤ 3500 in ∆ = 50 wide bins, for temperature map-noise levels of 10, 6.4 and 2 µK-arcmin. We divide the survey data into N real = 30, 50, or 100 uniform subsets. We show the results of different conditioning schemes on the errors in the covariance estimate, and how these uncertainties on the covariance matrix propagate to the best-fit parameters and parameter uncertainties. The most significant effect we find is an additional scatter in the best-fit point, beyond what is expected from the data likelihood. For a minimal conditioning strategy, N real = 30, and a temperature map-noise level of 10 µK-arcmin, we find the uncertainty on the recovered best fit parameter to be ×1.3 larger than the apparent posterior width from the likelihood (×1.2 larger than the uncertainty when the true covariance is used). Stronger priors on the covariance matrix reduce the misestimation of parameter uncertainties to < 1%. As expected, empirical estimates perform better with higher N real , ameliorating the adverse effects on parameter constraints.

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Cobaya: code for Bayesian analysis of hierarchical physical models

Cited by 360 publications

References 43 publications

Bias on Tensor-to-Scalar Ratio Inference With Estimated Covariance Matrices

Bias on Tensor-to-Scalar Ratio Inference With Estimated Covariance Matrices

The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: measurement of the growth rate of structure from the small-scale clustering of the luminous red galaxy sample

The Parameter-Level Performance of Covariance Matrix Conditioning in Cosmic Microwave Background Data Analyses

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