Global 21-cm Signal Extraction from Foreground and Instrumental Effects II: Efficient and Self-Consistent Technique for Constraining Nonlinear Signal Models. (arXiv:1912.02205v1 [astro-ph.CO])

<a href="http://arxiv.org/find/astro-ph/1/au:+Rapetti_D/0/1/0/all/0/1">David Rapetti</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Tauscher_K/0/1/0/all/0/1">Keith Tauscher</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Mirocha_J/0/1/0/all/0/1">Jordan Mirocha</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Burns_J/0/1/0/all/0/1">Jack O. Burns</a>

We present the completion of a data analysis pipeline that self-consistently

separates global 21-cm signals from large systematics using a pattern

recognition technique. In the first paper of this series, we obtain optimal

basis vectors from signal and foreground training sets to linearly fit both

components with the minimal number of terms that best extracts the signal given

its overlap with the foreground. In this second paper, we utilize the spectral

constraints derived in the first paper to calculate the full posterior

probability distribution of any signal parameter space of choice. The spectral

fit provides the starting point for a Markov Chain Monte Carlo (MCMC) engine

that samples the signal without traversing the foreground parameter space. At

each MCMC step, we marginalize over the weights of all linear foreground modes

and suppress those with unimportant variations by applying priors gleaned from

the training set. This method drastically reduces the number of MCMC

parameters, augmenting the efficiency of exploration, circumvents the need for

selecting a minimal number of foreground modes, and allows the complexity of

the foreground model to be greatly increased to simultaneously describe many

observed spectra without requiring extra MCMC parameters. Using two nonlinear

signal models, one based on EDGES observations and the other on

phenomenological frequencies and temperatures of theoretically expected

extrema, we demonstrate the success of this methodology by recovering the input

parameters from multiple randomly simulated signals at low radio frequencies

(10-200 MHz), while rigorously accounting for realistically modeled

beam-weighted foregrounds.

We present the completion of a data analysis pipeline that self-consistently

separates global 21-cm signals from large systematics using a pattern

recognition technique. In the first paper of this series, we obtain optimal

basis vectors from signal and foreground training sets to linearly fit both

components with the minimal number of terms that best extracts the signal given

its overlap with the foreground. In this second paper, we utilize the spectral

constraints derived in the first paper to calculate the full posterior

probability distribution of any signal parameter space of choice. The spectral

fit provides the starting point for a Markov Chain Monte Carlo (MCMC) engine

that samples the signal without traversing the foreground parameter space. At

each MCMC step, we marginalize over the weights of all linear foreground modes

and suppress those with unimportant variations by applying priors gleaned from

the training set. This method drastically reduces the number of MCMC

parameters, augmenting the efficiency of exploration, circumvents the need for

selecting a minimal number of foreground modes, and allows the complexity of

the foreground model to be greatly increased to simultaneously describe many

observed spectra without requiring extra MCMC parameters. Using two nonlinear

signal models, one based on EDGES observations and the other on

phenomenological frequencies and temperatures of theoretically expected

extrema, we demonstrate the success of this methodology by recovering the input

parameters from multiple randomly simulated signals at low radio frequencies

(10-200 MHz), while rigorously accounting for realistically modeled

beam-weighted foregrounds.

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