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We present the completion of a data analysis pipeline that self-consistentlyseparates global 21-cm signals from large systematics using a patternrecognition technique. In the first paper of this series, we obtain optimalbasis vectors from signal and foreground training sets to linearly fit bothcomponents with the minimal number of terms that best extracts the signal givenits overlap with the foreground. In this second paper, we utilize the spectralconstraints derived in the first paper to calculate the full posteriorprobability distribution of any signal parameter space of choice. The spectralfit provides the starting point for a Markov Chain Monte Carlo (MCMC) enginethat samples the signal without traversing the foreground parameter space. Ateach MCMC step, we marginalize over the weights of all linear foreground modesand suppress those with unimportant variations by applying priors gleaned fromthe training set. This method drastically reduces the number of MCMCparameters, augmenting the efficiency of exploration, circumvents the need forselecting a minimal number of foreground modes, and allows the complexity ofthe foreground model to be greatly increased to simultaneously describe manyobserved spectra without requiring extra MCMC parameters. Using two nonlinearsignal models, one based on EDGES observations and the other onphenomenological frequencies and temperatures of theoretically expectedextrema, we demonstrate the success of this methodology by recovering the inputparameters from multiple randomly simulated signals at low radio frequencies(10-200 MHz), while rigorously accounting for realistically modeledbeam-weighted foregrounds.

astrophysical journal/the astrophysical journal

Global 21-cm Signal Extraction from Foreground and Instrumental Effects  II: Efficient and Self-Consistent Technique for Constraining Nonlinear Signal  Models