Astronomical linear simulation based inference

Code and plots for the NST Physics Part III project "Astronomical Linear Simulation-based Inference"

Web reference: Galileo - Part III Projects supervised by Will Handley

Abstract

We develop the theoretical framework of Linear Simulation-based Inference (LSBI), an application of likelihood-free inference where the model is approximated by a linear function of its parameters and the noise is assumed to be Gaussian with zero mean. We obtain analytical expressions for the posterior distributions of hyperparameters of the linear likelihood in terms of samples drawn from a simulator. This method is applied to several toy models, and to emulated datasets for the Cosmic Microwave Background power spectrum and the sky-averaged 21cm hydrogen line. We find that convergence is achieved after $\mathcal{O}(10^4)$ simulations at most. Furthermore, LSBI is coupled with massive linear compression into a set of $n$ summary statistics, where $n$ is the number of parameters of the model, reducing the computational time by two to three orders of magnitude. Therefore, we demonstrate that it is possible to obtain significant information gain and generate posteriors that agree with the underlying parameters while maintaining explainability and intellectual oversight.

Dependencies

• Python 3.9+
• lsbi - GitHub, Documenation
• globalemu - GitHub, Documenation
• cmbemu - GitHub
• getdist - GitHub, Documentation

Citations

Handley et al, (2024) lsbi: Linear Simulation Based Inference.

Bevins, H., Handley, W. J., Fialkov, A., Acedo, E. D. L., and Javid, K. (2021). GLOBALEMU: A novel and robust approach for emulating the sky-averaged 21-cm signal from the cosmic dawn and epoch of reionisation. arXiv:2104.04336

Lewis, A. (2019). GetDist: a Python package for analysing Monte Carlo samples. arXiv preprint arXiv:1910.13970.