Constraining cosmological parameters with needlet internal linear combination maps. II. Likelihood-free inference on needlet internal linear combination power spectra

Standard cosmic microwave background (CMB) analyses constrain cosmological and astrophysical parameters by fitting parametric models to multifrequency power spectra (MFPS). However, such methods do not optimally weight maps in power spectrum (PS) measurements for non-Gaussian cosmic microwave background (CMB) foregrounds. We propose needlet internal linear combination (NILC), operating on wavelets with compact support in pixel and harmonic space, as a weighting scheme to yield more optimal parameter constraints. In a companion paper, we derived an analytic formula for the NILC map PS, which is physically insightful but computationally difficult to use in parameter inference pipelines. In this work, we analytically show that fitting parametric templates to MFPS and the harmonic ILC PS yields identical parameter constraints when the number of sky components equals or exceeds the number of frequency channels. We numerically show that, for Gaussian random fields, the same holds for the NILC PS. This suggests that NILC can reduce parameter error bars in the presence of non-Gaussian fields since it uses non-Gaussian information. As Gaussian likelihoods may be inaccurate, we use likelihood-free inference with neural posterior estimation. We show that performing inference with autospectra and cross-PS of NILC component maps as summary statistics yields smaller parameter error bars than inference with MFPS. For a model with CMB, an amplified thermal Sunyaev-Zel'dovich (tSZ) signal, and noise, we find a 60% reduction in the area of the 2D 68% confidence region for component amplitude parameters inferred from the NILC PS, as compared to inference from MFPS. Primordial $B$-mode searches are a promising application for our new method, as the amplitude of the non-Gaussian dust foreground is known to be larger than a potential signal.