This thesis is dedicated to advancing our understanding of the origin and evolution of the Universe by studying the cosmic microwave background (CMB), a light travelling through the cosmos since the dawn of time. The CMB contains rich information about the earliest time of the Universe, and informs us about the Universe as a whole due to it containing an imprint of the mass distribution of the Universe. We study this imprint through the development and application of a novel curved sky Bayesian analysis method. This comprehensive approach, inclusive of carefully treating biases, is designed to effectively handle real observational data and is aimed at tackling cosmological phenomena captured through the CMB.

Central to this thesis is the improvement of a Bayesian method, dubbed the Maximum a-posterior (MAP) lensing reconstruction. The MAP method optimally recovers the lensing information and is therefore an improvement over standard quadratic estimators (QE). Our Bayesian approach iteratively finds the MAP point of the deflection field, which makes this approach computationally more expensive than the QE. This is in particular true due to the full sky treatment for which spherical harmonics are the basis functions; their numerical calculation is more expensive than their flat sky counterpart, the Fourier basis.