Time Delay Cosmography with a Neural Ratio Estimator

TL;DR

This paper demonstrates that a Neural Ratio Estimator can accurately infer the Hubble constant from time delay cosmography data, offering a flexible and efficient alternative to traditional likelihood methods.

Contribution

The study introduces the application of a Neural Ratio Estimator to time delay cosmography for $H_0$ inference, showing comparable accuracy and the ability to handle complex models.

Findings

NRE accurately reproduces traditional likelihood results

NRE can be combined in population analyses without bias

NRE slightly overestimates uncertainties

Abstract

We explore the use of a Neural Ratio Estimator (NRE) to determine the Hubble constant ($H_0$) in the context of time delay cosmography. Assuming a Singular Isothermal Ellipsoid (SIE) mass profile for the deflector, we simulate time delay measurements, image position measurements, and modeled lensing parameters. We train the NRE to output the posterior distribution of $H_0$ given the time delay measurements, the relative Fermat potentials (calculated from the modeled parameters and the measured image positions), the deflector redshift, and the source redshift. We compare the accuracy and precision of the NRE with traditional explicit likelihood methods in the limit where the latter is tractable and reliable, using Gaussian noise to emulate measurement uncertainties in the input parameters. The NRE posteriors track the ones from the conventional method and, while they show a slight tendency to overestimate uncertainties, they can be combined in a population inference without bias.