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.

翻译：本文提出多提议椭圆切片采样，这是一种用于高斯先验贝叶斯推断的自适应多提议马尔可夫链蒙特卡洛方法。本方法通过以下两点推广了椭圆切片采样算法：1）允许在每个自适应步骤中并行采样多个候选提议；2）基于距离感知的转移矩阵进行接受步骤，该矩阵可优先选择远离当前状态的提议。这允许在状态空间中进行更大范围的移动并实现更快的自适应调整，对于计算代价高昂的似然函数几乎不增加实际计算时间，从而改善了混合性能。我们还提供了理论论证和实验结果，表明该方法具有维度鲁棒的混合特性，使其特别适用于贝叶斯偏微分方程反演问题。