Cosmic Microwave Background and Large Scale Structure Power Spectrum Estimation with Guided Hamiltonian Sampling

Abstract

Cosmological surveys return large datasets probing different epochs in the evolutionary history of the universe. It is therefore unfeasible to use brute force methods to analyse this data. Aim: In this project, we test the applicability of the Guided Hamiltonian Sampler (GHS), a modified Monte Carlo (MC) sampling process on galaxy clustering data. We compare its performance and efficiency with conventional methods used for cosmic microwave background (CMB) and large scale structure (LSS) power spectrum estimation. We apply the sampler to observed data from surveys like SDSS, Dark Energy Survey etc. Method: GHS suppresses the random walk nature of traditional MC sampling techniques by obeying the hamiltonian equations of motion in the sample space. It is an extension of the Hamiltonian Monte Carlo (HMC). It removes the need to fine-tune a million parameters in HMC and only requires a single parameter, the dimensionality scaling factor. This makes it an exciting method to use on higher dimensional datasets. Result: After analysing sampler performance under various configurations and input parameters, we find that GHS returns fiducial values in the domain of high spatial galaxy population. Comparing it with conventional methods like pseudo Cl, we see that the error bars from the sampler are similar in magnitude. Using GHS on datasets like SDSS and DES, we confirm the excess of power observed on the largest scales in the literature (Thomas et al. [2011], Huterar et al. [2013]).