Compressed 'CMB-lite' Likelihoods Using Automatic Differentiation
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929718618488832 |
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| author | Balkenhol, L. |
| author_facet | Balkenhol, L. |
| contents | The compression of multi-frequency cosmic microwave background (CMB) power spectrum measurements into a series of foreground-marginalised CMB-only band powers allows for the construction of faster and more easily interpretable 'lite' likelihoods. However, obtaining the compressed data vector is computationally expensive and yields a covariance matrix with sampling noise. In this work, we present an implementation of the CMB-lite framework relying on automatic differentiation. The technique presented reduces the computational cost of the lite likelihood construction to one minimisation and one Hessian evaluation, which run on a personal computer in about a minute. We demonstrate the efficiency and accuracy of this procedure by applying it to the differentiable SPT-3G 2018 TT/TE/EE likelihood from the candl library. We find good agreement between the marginalised posteriors of cosmological parameters yielded by the resulting lite likelihood and the reference multi-frequency version for all cosmological models tested; the best-fit values shift by $<0.1\,σ$, where $σ$ is the width of the multi-frequency posterior, and the inferred parameter error bars match to within $<10\%$. We publicly release the SPT-3G 2018 TT/TE/EE lite likelihood and a python notebook showing its construction at https://github.com/Lbalkenhol/candl . |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_00826 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Compressed 'CMB-lite' Likelihoods Using Automatic Differentiation Balkenhol, L. Cosmology and Nongalactic Astrophysics The compression of multi-frequency cosmic microwave background (CMB) power spectrum measurements into a series of foreground-marginalised CMB-only band powers allows for the construction of faster and more easily interpretable 'lite' likelihoods. However, obtaining the compressed data vector is computationally expensive and yields a covariance matrix with sampling noise. In this work, we present an implementation of the CMB-lite framework relying on automatic differentiation. The technique presented reduces the computational cost of the lite likelihood construction to one minimisation and one Hessian evaluation, which run on a personal computer in about a minute. We demonstrate the efficiency and accuracy of this procedure by applying it to the differentiable SPT-3G 2018 TT/TE/EE likelihood from the candl library. We find good agreement between the marginalised posteriors of cosmological parameters yielded by the resulting lite likelihood and the reference multi-frequency version for all cosmological models tested; the best-fit values shift by $<0.1\,σ$, where $σ$ is the width of the multi-frequency posterior, and the inferred parameter error bars match to within $<10\%$. We publicly release the SPT-3G 2018 TT/TE/EE lite likelihood and a python notebook showing its construction at https://github.com/Lbalkenhol/candl . |
| title | Compressed 'CMB-lite' Likelihoods Using Automatic Differentiation |
| topic | Cosmology and Nongalactic Astrophysics |
| url | https://arxiv.org/abs/2412.00826 |