多提案椭圆切片采样
Multiproposal Elliptical Slice Sampling
AI总结：
多提案椭圆切片采样是一种自调整的马尔可夫链蒙特卡洛方法，通过并行采样多个候选提案和基于距离信息的转移矩阵，提高了贝叶斯推断中高斯先验下的混合效率。
摘要：
我们介绍了一种名为多提案椭圆切片采样(self-tuning multiproposal Markov chain Monte Carlo)的方法，这是一种用于具有高斯先验的贝叶斯推断的自调整多提案马尔可夫链蒙特卡洛方法。我们的方法通过两个方面扩展了椭圆切片采样算法：1）在每个自调整步骤中允许同时采样多个候选提案；2）基于一种距离信息的转移矩阵来决定接受步骤，该矩阵可以倾向于远离当前状态的提案。这使得在状态空间中能够进行更大的移动并加快自调整过程，而在昂贵的似然函数下几乎不增加实际时间，从而提高了混合性。我们还提供了理论论证和实验结果，表明该算法具有对维度鲁棒的混合行为，使其特别适用于贝叶斯偏微分方程反问题。
英文摘要：
We introduce Multiproposal Elliptical Slice Sampling, a self-tuning multiproposal Markov chain Monte Carlo method for Bayesian inference with Gaussian priors. Our method generalizes the Elliptical Slice Sampling algorithm by 1) allowing multiple candidate proposals to be sampled in parallel at each self-tuning step, and 2) basing the acceptance step on a distance-informed transition matrix that can favor proposals far from the current state. This allows larger moves in state space and faster self-tuning, at essentially no additional wall clock time for expensive likelihoods, and results in improved mixing. We additionally provide theoretical arguments and experimental results suggesting dimension-robust mixing behavior, making the algorithm particularly well suited for Bayesian PDE inverse problems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
