Nested Slice Sampling

Nested Sampling is a powerful meta Bayesian inference algorithm known for its ability to estimate the marginal likelihood of a model and perform parameter inference, even for complex multimodal distributions. In this paper, we refine the formulation of Nested Sampling in the context of slice sampling, leading to a novel vectorized version of the algorithm that leverages GPU acceleration for improved efficiency in machine learning applications. We demonstrate that this vectorized Nested Slice Sampling algorithm can exploit parallelization opportunities to substantially reduce runtime while maintaining sampling accuracy. The performance of the approach is evaluated on a range of challenging benchmark problems, showing significant improvements in sampling efficiency and scalability to high dimensions. The proposed vectorized Nested Sampling algorithm opens up new possibilities for applying Nested Sampling to large-scale machine learning problems where efficient Bayesian inference is critical. We provide an open-source implementation of our method to facilitate adoption and reproducibility.