Bayesian inference on the sphere beyond statistical isotropy

Abstract

Abstract. We present a general method for Bayesian inference of the underlying covariance structure of random fields on a sphere. We employ the Bipolar Spherical Harmonic (BipoSH) representation of general covariance structure on the sphere. We illustrate the efficacy of the method as a principled approach to assess violation of statistical isotropy (SI) in the sky maps of Cosmic Microwave Background (CMB) fluctuations. SI violation in observed CMB maps arise due to known physical effects such as Doppler boost and weak lensing; yet unknown theoretical possibilities like cosmic topology and subtle violations of the cosmological principle, as well as, expected observational artefacts of scanning the sky with a non-circular beam, masking, foreground residuals, anisotropic noise, etc. We explicitly demonstrate the recovery of the input SI violation signals with their full statistics in simulated CMB maps. Our formalism easily adapts to exploring parametric physical models with non-SI covariance, as we illustrate for the inference of the parameters of a Doppler boosted sky map. Our approach promises to provide a robust quantitative evaluation of the evidence for SI violation related anomalies in the CMB sky by estimating the BipoSH spectra along with their complete posterior.arXiv:1509.07137v1 [astro-ph.CO]

The search for statistical anisotropy in the gravitational-wave background with pulsar timing arrays

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A Bayesian Approach for Detection of Isotropy Violation of a Random Field Over a Sphere

“…On the other hand, Hamiltonian Monte Carlo (HMC) technique [1,[11][12][13] is based on Classical Hamiltonian Mechanics and if a group of particles is placed in the region will faithfully map the potential distribution given that all of them start from random velocity following normal distribution with zero mean and unit variance. The HMC method can sample the distribution more effectively even in very high dimensional space in comparison to the conventional MCMC methods.…”

“…Choice of m a lm and m A LM ll decides the stability of the integration process. The error propagation equation demands that for integratingȧ lm , hM −1 lml m (S −1 lml m + N −1 l ) < 2.3, where h is the step size in the integration process and M lml m is the mass matrix for a lm [1,15] . As we define an individual mass to each of a lm , the mass matrix, M lml m is diagonal.…”

“…We develop our analysis strongly motivated by the analysis of cosmic microwave background (CMB) sky maps to infer the statistical isotropy (SI) of our observed universe. However, the methodology is applicable to Bayesian inference for other cosmological studies, and more widely to any study involving a scalar random field on the sphere [1] .…”

Magnetic white dwarfs: Observations, theory and future prospects

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