MUSE: A new algorithm for accelerated Bayesian inference with applications to CMB and large-scale-structure correlations

Bayesian inference offers a powerful framework for extracting cosmological information from observations which is automatically statistically optimal and straightforward to construct. Its main challenge is high computational cost, particularly for cosmological applications, which feature large numbers of parameter dimensions and non-Gaussian Bayesian posterior distributions. Here, I present a new algorithm, the Marginal Unbiased Score Expansion (MUSE) method, which accelerates inference over state-of-the-art Hamiltonian Monte Carlo methods by as much as factors of 500.

I will describe the algorithm and its associated software packages, with an aim to give listeners the needed understanding to apply to their own Bayesian problems in cosmology. I will then present some example applications. First, in the machine learning domain, it can be used to speed up Bayesian neural network analyses. Second, it has, for the first time, made possible a Bayesian analysis of high-resolution lensed CMB data. I will introduce its application to South Pole Telescope data, where it is being used to reduce lensing reconstruction noise by factor of ~2 compared to standard quadratic estimator approaches and will soon provide our tightest ground-based constraints on cosmological parameters such as the Hubble constant (an in-depth discussion of this is given in a separate talk). I will also describe our plans to extend this analysis to incorporate BICEP/Keck data and eventually CMB-S4 data, where it will provide the necessary delensing allowing CMB-S4 to achieve its stated goals for primordial gravitational wave detection. Finally, I will describe preliminary work using MUSE to perform the first Bayesian and optimal cross-correlation analysis between CMB data and large-scale structure.