# mathttemuflow: Normalising Flows for Joint Cosmological Analysis

arXiv: https://arxiv.org/abs/2409.01407 · HTML: https://mlsanity.com/paper/2409.01407/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 67 references that are in the map.
- First posted on arXiv 2 Sep 2024.

## Builds on (most cited first, 5 of 5)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Demystifying MMD GANs](https://mlsanity.com/paper/1801.01401/) (2018)
- [Machine learning assisted Bayesian model comparison: learnt harmonic mean estimator](https://mlsanity.com/paper/2111.12720/) (2021)
- [Learned harmonic mean estimation of the Bayesian evidence with normalizing flows](https://mlsanity.com/paper/2405.05969/) (2024)
- [Bayesian evidence estimation from posterior samples with normalizing flows](https://mlsanity.com/paper/2404.12294/) (2024)

## Built on by (most cited first, 2 of 2)

- [Cosmology with Persistent Homology: Parameter Inference via Machine Learning](https://mlsanity.com/paper/2412.15405/) (2024)
- [Recovering Weak Signals with Normalizing Flows](https://mlsanity.com/paper/2609.06382/) (2026)

## Abstract (arXiv)

Given the growth in the variety and precision of astronomical datasets of interest for cosmology, the best cosmological constraints are invariably obtained by combining data from different experiments. At the likelihood level, one complication in doing so is the need to marginalise over large-dimensional parameter models describing the data of each experiment. These include both the relatively small number of cosmological parameters of interest and a large number of "nuisance" parameters. Sampling over the joint parameter space for multiple experiments can thus become a very computationally expensive operation. This can be significantly simplified if one could sample directly from the marginal cosmological posterior distribution of preceding experiments, depending only on the common set of cosmological parameters. In this paper, we show that this can be achieved by emulating marginal posterior distributions via normalising flows. The resulting trained normalising flow models can be used to efficiently combine cosmological constraints from independent datasets without increasing the dimensionality of the parameter space under study. We show that the method is able to accurately describe the posterior distribution of real cosmological datasets, as well as the joint distribution of different datasets, even when significant tension exists between experiments. The resulting joint constraints can be obtained in a fraction of the time it would take to combine the same datasets at the level of their likelihoods. We construct normalising flow models for a set of public cosmological datasets of general interests and make them available, together with the software used to train them, and to exploit them in cosmological parameter inference.