MR. SANTANU DAS

If the CMB sky is statistically isotropic, the angular power spectrum (Cl) is sufficient to provide the complete statistics of the CMB temperature fluctuations. However, in presence of statistical isotropy (SI) violation, apart from Cl, we need the Bipolar Spherical Harmonics (BipoSH) coefficients for proper representation of the sky statistics. While methods are developed for estimating the Cl from a observed sky map, they do not extend to estimation of BipoSH coefficients. Hence, a Bayesian statistics of the BipoSH coefficients of the CMB sky is not measured. Here, we present a novel method for fast optimal estimation of the temperature angular power spectrum along with the BipoSH coefficients from observed skymap, by minimizing the likelihood with respect to both Cl and BipoSH coefficients using a complete Bayesian technique. We use a Hamiltonian Monte Carlo (HMC) sampler for obtaining samples. The algorithm estimates Cl up to a very high l even in presence of high noise. It also estimates the BipoSH coefficients adequately up to high l. We test the algorithm on the simulated dipole modulation signal, Doppler Boost signal as detected on Planck and the beam anisotropy signal as detected on WMAP-7, with perfect recovery.