Non-reversible and generative sampling algorithms. Application to the inference of cosmological parameters
- Authors
- Publication Date
- Sep 25, 2024
- Source
- HAL
- Keywords
- Language
- English
- License
- Unknown
- External links
Abstract
This PhD thesis is dedicated to the development and analysis of sampling algorithms with applications to the inference of cosmological parameters. We first review the mathematical tools as well as the cosmological framework. Then, we introduce two algorithms. The first one is called PDMC-BORG. It is a non-reversible Markov Chain Monte Carlo sampler used for performing large-scale structure inference. It relies on the BORG framework developed by the Aquila consortium to infer the primordial density field from astronomical data. We detail the main features of the algorithm, explain how to tune it and show that its performance are similar to that of a baseline Hamiltonian Monte Carlo sampler. Then, we introduce a fixed-kinetic energy variant of Neural Hamiltonian Flows, a type of generative model that uses symplectic Hamiltonian transformations to map a base distribution on any target. Our modification allows to enhance interpretability of the model while reducing its numerical complexity. We test its performance in image generation and explain how to use Neural Hamiltonian Flows and its variants in the context of Bayesian inference, illustrating the method on the inference of two cosmological parameters from supernovae observations.
