Dear Developers
My name is David and I would like to propose a new extended feature for UQLab called “Nested Sampling”. As the name suggests, my proposal is to develop a new toolbox for nested sampling algorithms. Nested Sampling is a comparably new technique for Bayesian Inversion and in general multidimensional integration. At the moment, it is applied in many research fields such as cosmology, gravitational-wave astronomy and materials science. Nested sampling is known to manage hard high-dimensional likelihood functions with multiple modes and highly localized likelihood masses. Moreover, it can also estimate the evidence similarly to SSE. The latter is particularly interesting for Bayesian model comparison applications. A good overview about this topic is given by Ashton et al. [1] and Buchner [2].
In my opinion, nested sampling would perfectly fit into the framework of Bayesian inversion and complement the already implemented MCMC and Stochastic spectral embedding (SEE) algorithms. Due to the many open-source codes available [3-5], the implementation of these algorithms should be comparably easy.
From a scientific perspective, it would be really interesting to compare MCMC, SSE and nested sampling for Bayesian inversion problems, especially for more challenging toy problems as featured by Wagner et al. [6].
Let me know, what you think about my idea.
Cheers,
David
[1] https://doi.org/10.1038/s43586-022-00121-x
[2] https://doi.org/10.48550/arxiv.2101.09675
[3] https://doi.org/10.1093/MNRAS/STAA278
[4] https://doi.org/10.1093/MNRAS/STV1911
[5] https://doi.org/10.21105/JOSS.03001
[6] https://doi.org/10.1016/J.JCP.2021.110141