Bayesian noise estimation for non-ideal CMB experiments

TL;DR

This paper introduces a Bayesian Gibbs sampling method for accurately estimating the time-domain noise covariance in CMB experiments, accommodating data gaps and other complexities, validated with simulated data.

Contribution

It presents a novel Bayesian framework using Gibbs sampling for noise estimation in CMB data, including support for gaps and marginalization over templates and confusion.

Findings

Unbiased noise parameter reconstruction demonstrated with simulations.

Efficient processing time: 3 seconds for maximum posterior, 21 seconds for uncertainties.

Supports gaps and marginalization over CMB fluctuations.

Abstract

We describe a Bayesian framework for estimating the time-domain noise covariance of CMB observations, typically parametrized in terms of a 1/f frequency profile. This framework is based on the Gibbs sampling algorithm, which allows for exact marginalization over nuisance parameters through conditional probability distributions. In this paper we implement support for gaps in the data streams and marginalization over fixed time-domain templates, and also outline how to marginalize over confusion from CMB fluctuations, which may be important for high signal-to-noise experiments. As a by-product of the method, we obtain proper constrained realizations, which themselves can be useful for map making. To validate the algorithm, we demonstrate that the reconstructed noise parameters and corresponding uncertainties are unbiased using simulated data. The CPU time required to process a single data stream of 100 000 samples with 1000 samples removed by gaps is 3 seconds if only the maximum posterior parameters are required, and 21 seconds if one also want to obtain the corresponding uncertainties by Gibbs sampling.