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tokens: the width of the frequency band, andIn our case, and , so ν 0 = 80 MHz and δ ν = 40 MHz. To seed the beam variations in our training set, we draw a 0 , a 1 , and a 2 from independent normal distributions,with the means and standard deviations μ k and σ k given in Table 3 . An extra constraint is applied to exclude FWHM( ν ) curves which dip below 15° in the 40–120 MHz band. The resulting training set of FWHM curves is shown in Figure 3 . We simulate the beam-weighted foreground temperature for ten different bins in LST by smearing the map through LST before computing the spectra. 20 20 By smearing, we refer to averaging many rotations of the foreground map corresponding to LSTs between the edges of each LST bin. The spectra from the 10 LST bins are then concatenated into the final data vector. It is important to note here that the Legendre-polynomial based toy model used to generate the beam training set in this paper is a placeholder for performing detailed electromagnetic simulations specific to the antenna used by the experiment being analyzed. Such simulations can output both antenna power patterns and S -parameters while accounting for effects such as ground plane interactions, scattering/reflections from nearby objects, and local soil properties. Since the gain, G ν , represents the instrument’s transducer gain, which includes the antenna reflection coefficient (Nhan et al. 2019 ), these simulations will also inform the model of the gain. In addition, if these simulations find that a given antenna design is sufficiently inefficient, the noise level from Equation ( 10 ) could be modified to account for the fact that the system temperature of an instrument with that antenna would not be dominated by beam-weighted foreground sources. 3. Signal training set : is formed from a training set where each curve is created by applying the turning point nonlinear signal model to a sample from the prior distribution of its parameters (see Section 4.2 , Figure 2 , and Table 2 ). Figure 3. Ten percent of the training set of 500 beam FWHM. The curves are quadratic Legendre polynomials with coefficient distributions given in Table 3 . Table 3 Parameters of Legendre Coefficient Distributions. Note: See Equations ( 14 )–( 16 ). 5. Results This section lays out the results of applying the general AMLP method described in Section 2 to the procedure put forth in Section 3 for fitting sky-averaged radio data measured with a nonideal receiver using the models laid out in Section 4 . The initial fit using the linear signal model (following Section 3.2.2 ) is shown in Section 5.1 and the final fit using the nonlinear signal model (following Section 3.2.4 ) is shown in Section 5.2 . 5.1. Fit with Linear Signal Model The signal uncertainties implied by the first MCMC fit with the linear signal model are shown in Figure 4 . The main mode of uncertainty is line-like, with a width of approximately 50 mK. This width comes from the similarity, or overlap, between the