We present Nested Sampling with Slice-within-Gibbs (NS-SwiG), an algorithm for Bayesian inference and evidence estimation in high-dimensional models whose likelihood admits a factorization, such as hierarchical Bayesian models. We construct a procedure to sample from the likelihood-constrained prior using a Slice-within-Gibbs kernel: an outer update of hyperparameters followed by inner block updates over local parameters. A likelihood-budget decomposition caches per-block contributions so that each local update checks feasibility in constant time rather than recomputing the global constraint at linearly growing cost. This reduces the per-replacement cost from quadratic to linear in the number of groups, and the overall algorithmic complexity from cubic to quadratic under standard assumptions. The decomposition extends naturally beyond independent observations, and we demonstrate this on Markov-structured latent variables. We evaluate NS-SwiG on challenging benchmarks, demonstrating scalability to thousands of dimensions and accurate evidence estimates even on posterior geometries where state-of-the-art gradient-based samplers can struggle.

翻译：本文提出基于切片吉布斯采样的嵌套抽样算法，该算法适用于似然函数可分解的高维模型（如层次贝叶斯模型）的贝叶斯推断与证据估计。我们构建了一种利用切片吉布斯核从似然约束先验中采样的流程：先对超参数进行外部更新，再对局部参数进行内部块更新。通过似然预算分解缓存各块的贡献度，使得每次局部更新可在常数时间内检验可行性，而非以线性增长的成本重新计算全局约束。这将每次替换成本从组数量的二次方降至线性，且在标准假设下整体算法复杂度从三次方降至二次方。该分解方法可自然扩展至非独立观测情形，我们在马尔可夫结构隐变量上验证了这一点。我们在具有挑战性的基准测试中评估了该算法，证明其可扩展至数千维度，并在当前最先进的基于梯度的采样器可能失效的后验几何结构上仍能获得精确的证据估计。