In SICRET, we take a step back from raw light curves, astrophysical modelling, and real data and look to the future: the aim of this chapter is to prove that a truncated marginal neural ratio estimation (TMNRE) analysis can deliver accurate and precise posteriors for cosmological parameters from future-sized data sets. To this end, we employ iterative truncation to systematically restrict the prior ranges of the global parameters of the model and deliver maximally precise and still accurate results with a simple fully connected multi-layer perceptron network. We test the framework on mock data of increasing sizes from a deceptively simple Bayesian hierarchical model for a purely photometric SN Ia survey, showing that SBI constraints remain unbiased and exhibit optimal scaling up to 100 000 SNæ Ia, while likelihood-based inference—with a simplified model that linearly propagates significant photometric redshift uncertainties so as to remain computationally feasible—wanders catastrophically astray. Following global inference, we infer marginally, but simultaneously, the 100 000 SNspecific standardised absolute brightnesses (which are the target of conventional fitting/standardisation analyses) and demonstrate that they too have the expected accuracy and precision. Finally, once again, we validate and calibrate our results for the parameters of ΛCDM cosmology as an added measure of their robustness.

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SN Ia cosmology with TMNRE (scaling to 100 000)

  • Konstantin Karchev

摘要

In SICRET, we take a step back from raw light curves, astrophysical modelling, and real data and look to the future: the aim of this chapter is to prove that a truncated marginal neural ratio estimation (TMNRE) analysis can deliver accurate and precise posteriors for cosmological parameters from future-sized data sets. To this end, we employ iterative truncation to systematically restrict the prior ranges of the global parameters of the model and deliver maximally precise and still accurate results with a simple fully connected multi-layer perceptron network. We test the framework on mock data of increasing sizes from a deceptively simple Bayesian hierarchical model for a purely photometric SN Ia survey, showing that SBI constraints remain unbiased and exhibit optimal scaling up to 100 000 SNæ Ia, while likelihood-based inference—with a simplified model that linearly propagates significant photometric redshift uncertainties so as to remain computationally feasible—wanders catastrophically astray. Following global inference, we infer marginally, but simultaneously, the 100 000 SNspecific standardised absolute brightnesses (which are the target of conventional fitting/standardisation analyses) and demonstrate that they too have the expected accuracy and precision. Finally, once again, we validate and calibrate our results for the parameters of ΛCDM cosmology as an added measure of their robustness.