ner_tags: O O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O B-Model O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O B-CelestialObject O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
tokens: an antenna with cos 2 beam would have a maximum temperature at the LST when the Galactic center is at zenith. This also corresponds to the spectrum having the largest rms residual among the various mock spectra considered here. For various large-area samplings of the sky, we have thus demonstrated that the foreground component in a beam-averaged spectrum is adequately describable by an MS function. Thus for observations with a frequency-independent beam, MS functions can be used to separate foregrounds from the global EoR signal. We next discuss mathematical statistical detection based on MS-form modeling of foregrounds. 5. On the Detection of the Global Reionization Signal A mock observation of the radio sky as observed by a cos 2 beam is shown in Figures 14 . A GMOSS model for the sky has been adopted and CMB with a spectral distortion corresponding to generic global EoR has been added. We fit this mock observation of the sky spectrum with a function given by the sum of an MS function to model the foreground and a Planck spectrum to account for the undistorted CMB, as described by Equation ( 9 ). We use the downhill simplex (Nelder Mead 1965 ) optimization algorithm to iteratively fit this model to the synthetic spectrum, adopting a successive approximation strategy. The MS polynomial is expressed as a polynomial expansion about a frequency given by the parameter . The first iteration fits a function that has four parameters: the CMB temperature , the pivot frequency , and two coefficients that describe a single power law for the foreground. We successively include more terms using the optimized parameters from the previous iteration as initial guess and zero for the new coefficient introduced. The residuals on subtracting a model with a Planckian function and MS functions of degree 2, 5, 7, 8, 10, and 15 are also shown in Figure 14 . This may be compared to the residuals obtained above on fitting unconstrained polynomials to the same mock observation containing the EoR signal, which was shown in Figure 6 . As noted earlier, for the case where the foregrounds were modeled as unconstrained polynomials, the residual amplitude gets progressively lower with increasing polynomial order and there are additional turning points introduced. On the other hand, while using MS functions, the residual remains unchanged once the MS function encounters a shape that cannot be described as smooth and thenceforth increasing the order of the MS function no longer changes the residual. This would continue to be the case on fitting the spectrum with MS functions of arbitrarily higher order. The residual recovered on fitting the mock spectrum with such components that may accurately model the undistorted CMB and foreground appears qualitatively similar to the adopted global EoR signal, which was included in the simulation. We now proceed to quantify the confidence in signal detection and the likelihood of false positives. Figure 14. (a) Mock spectrum generated