# Bayesian power spectrum estimation at the Epoch of Reionization

## TL;DR

This paper presents a new Bayesian method for estimating the three-dimensional power spectrum during the Epoch of Reionization from interferometric data, capable of handling small and large sets of spatial frequency modes efficiently.

## Contribution

It introduces a versatile Bayesian framework with two approaches for power spectrum estimation, including Hamiltonian Monte Carlo sampling for large mode sets, demonstrated on simulated data.

## Key findings

- Including a strong foreground does not affect EoR power spectrum estimates.
- The method effectively recovers the EoR signal in simulated observations.
- Two sampling strategies are validated for different data complexities.

## Abstract

We introduce a new method for performing robust Bayesian estimation of the three-dimensional spatial power spectrum at the Epoch of Reionization (EoR), from interferometric observations. The versatility of this technique allows us to present two approaches. First, when the observations span only a small number of independent spatial frequencies ($k$-modes) we sample directly from the spherical power spectrum coefficients that describe the EoR signal realisation. Second, when the number of $k$-modes to be included in the model becomes large, we sample from the joint probability density of the spherical power spectrum and the signal coefficients, using Hamiltonian Monte Carlo methods to explore this high dimensional ($\sim$ 20000) space efficiently. This approach has been successfully applied to simulated observations that include astrophysically realistic foregrounds in a companion publication (Sims et al. 2016). Here we focus on explaining the methodology in detail, and use simple foreground models to both demonstrate its efficacy, and highlight salient features. In particular, we show that including an arbitrary flat spectrum continuum foreground that is $10^8$ times greater in power than the EoR signal has no detectable impact on our parameter estimates of the EoR power spectrum recovered from the data.