Reliable Parameter Inference for the Epoch of Reionization using Balanced Neural Ratio Estimation

TL;DR

The paper addresses miscalibration in EoR parameter inference that arises when using a multivariate Gaussian likelihood for Ly$\alpha$ forest statistics. It applies Balanced Neural Ratio Estimation, a Simulation-Based Inference method, to a two-parameter EoR model $(\lambda_{\mathrm{mfp}}, \langle F \rangle)$ at $z=5.5$, trained on large sets of forward-modeled mocks and calibrated via TARP and SBC. The BNRE posteriors are significantly better calibrated than Gaussian posteriors, and the method remains robust under variations of the BNRE hyperparameter $\gamma$; a comparison with Neural Posterior Estimation shows BNRE’s superior calibration and computational efficiency in this setup. This work demonstrates SBI’s practical applicability to cosmological modeling and provides a path toward statistically robust inferences in more complex EoR frameworks with minimal changes to existing forward-modeling pipelines.

Abstract

We present an application of the Balanced Neural Ratio Estimation (BNRE) algorithm to improve the statistical validity of parameter estimates used to characterize the Epoch of Reionization, where the common assumption of a multivariate Gaussian likelihood leads to overconfident and biased posterior distributions. Using a two-parameter model of the Ly$α$ forest autocorrelation function, we show that BNRE yields posterior distributions that are significantly better calibrated than those obtained under the Gaussian likelihood assumption, as verified through the Test of Accuracy with Random Points (TARP) and Simulation-Based Calibration (SBC) diagnostics. These results demonstrate the potential of Simulation-Based Inference (SBI) methods, and in particular BNRE, to provide statistically robust parameter constraints within existing astrophysical modeling frameworks.

Figures (7)

• Figure 1: Given a set of parameters $\boldsymbol{\theta}$, the model generates a set of mock Ly$\alpha$ forest autocorrelation functions. These mocks can be used to: (i) compute the mean autocorrelation function $\boldsymbol{\xi}_{m}$ and the corresponding covariance matrix $\boldsymbol{\Sigma}_{\boldsymbol{\xi}}$ required to evaluate an assumed multivariate Gaussian likelihood, or (ii) train a neural ratio estimator (BNRE in this study). Both approaches yield posterior distributions via MCMC sampling (emcee in the Gaussian case, and HMC/NUTS in the BNRE case).
• Figure 2: Corner plots of the posterior distributions obtained with both inference methods for two separate mock observations. The red text under the legend indicates the corresponding true parameter values $(\lambda_{\mathrm{mfp}}, \langle F \rangle)_{\mathrm{true}}$. Contours denote the 68% and 95% credible regions.
• Figure 3: Left: SBC rank histograms for $\lambda_{\text{mfp}}$ and $\langle F \rangle$ obtained by both parameter inference methods. Uniform posteriors indicate correct calibration, with the shaded region showing the expected range under sampling variability. Right: Coverage probabilities obtained by using TARP on a set of posterior distributions obtained with both methods. The shaded regions represent the respective 16th--84th percentile ranges obtained via bootstrap sampling.
• Figure 4: Corner plots of the posterior distributions obtained using the Guassian likelihood and BNRE with $\gamma=100.0$ for four randomly selected mock observations. The true parameter values are shown in red for each case respectively. The contours denote the 68% and 95% credible regions.
• Figure 5: Left: SBC rank histograms for $\lambda_{\text{mfp}}$ and $\langle F \rangle$ obtained using BNRE with $\gamma=10$. Uniform posteriors indicate correct calibration, with the shaded region showing the expected range under sampling variability. Right: Coverage probabilities obtained by using TARP on a set of posterior distributions obtained with both methods. The shaded regions represent the respective 16th--84th percentile ranges obtained via bootstrap sampling.