arXiv subjects

William J. Handley

Publications and source records attributed to William J. Handley.

3 recordsLinked to original sources

arXiv2026

Calibrating Bayesian Tension Statistics using Neural Ratio Estimation

When fits of the same physical model to two different datasets disagree, we call this tension. Several apparent tensions in cosmology have occupied researchers in recent years, and a number of different metrics have been proposed to quantify tension. Many of these metrics suffer from limiting assumptions, and correctly calibrating these is essential if we want to successfully determine whether discrepancies are significant. A commonly used metric of tension is the evidence ratio R. The statistic has been widely adopted by the community as a Bayesian way of quantifying tensions, however, it has a non-trivial dependence on the prior that is not always accounted for properly. We show that this can be calibrated out effectively with Neural Ratio Estimation. We demonstrate our proposed calibration technique with an analytic example, a toy example inspired by 21-cm cosmology, and with observations of the Baryon Acoustic Oscillations from the Dark Energy Spectroscopic Instrument (DESI) and the Sloan Digital Sky Survey (SDSS). We find no significant tension between DESI and SDSS.

astro-ph.CO↗

arXiv2025

Accounting for Noise and Singularities in Bayesian Calibration Methods for Global 21-cm Cosmology Experiments

Due to the large dynamic ranges involved with separating the cosmological 21-cm signal from the Cosmic Dawn from galactic foregrounds, a well-calibrated instrument is essential to avoid biases from instrumental systematics. In this paper we present three methods for calibrating a global 21-cm cosmology experiment using the noise wave parameter formalisation to characterise a low noise amplifier including a careful consideration of how calibrator temperature noise and singularities will bias the result. The first method presented in this paper builds upon the existing conjugate priors method by weighting the calibrators by a physically motivated factor, thereby avoiding singularities and normalising the noise. The second method fits polynomials to the noise wave parameters by marginalising over the polynomial coefficients and sampling the polynomial orders as parameters. The third method introduces a physically motivated noise model to the marginalised polynomial method. Running these methods on a suite of simulated datasets based on the REACH receiver design and a lab dataset, we found that our methods produced a calibration solution which is equally as or more accurate than the existing conjugate priors method when compared with an analytic estimate of the calibrator's noise. We find in the case of the measured lab dataset the conjugate priors method is biased heavily by the large noise on the shorted load calibrator, resulting in incorrect noise wave parameter fits. This is mitigated by the methods introduced in this paper which calibrate the validation source spectra to within 5% of the noise floor.

astro-ph.IM↗

arXiv2023

Marginal Post Processing of Bayesian Inference Products with Normalizing Flows and Kernel Density Estimators

Bayesian analysis has become an indispensable tool across many different cosmological fields including the study of gravitational waves, the Cosmic Microwave Background and the 21-cm signal from the Cosmic Dawn among other phenomena. The method provides a way to fit complex models to data describing key cosmological and astrophysical signals and a whole host of contaminating signals and instrumental effects modelled with `nuisance parameters'. In this paper, we summarise a method that uses Masked Autoregressive Flows and Kernel Density Estimators to learn marginal posterior densities corresponding to core science parameters. We find that the marginal or 'nuisance-free' posteriors and the associated likelihoods have an abundance of applications including; the calculation of previously intractable marginal Kullback-Leibler divergences and marginal Bayesian Model Dimensionalities, likelihood emulation and prior emulation. We demonstrate each application using toy examples, examples from the field of 21-cm cosmology and samples from the Dark Energy Survey. We discuss how marginal summary statistics like the Kullback-Leibler divergences and Bayesian Model Dimensionalities can be used to examine the constraining power of different experiments and how we can perform efficient joint analysis by taking advantage of marginal prior and likelihood emulators. We package our multipurpose code up in the pip-installable code margarine for use in the wider scientific community.

astro-ph.IM↗