Bayesian inference remains one of the most important tool-kits for any scientist, but increasingly expensive likelihood functions are required for ever-more complex experiments, raising the cost of generating a Monte Carlo sample of the posterior. Recent attention has been directed towards the use of emulators of the posterior based on Gaussian Process (GP) regression combined with active sampling to achieve comparable precision with far fewer costly likelihood evaluations. Key to this approach is the batched acquisition of proposals, so that the true posterior can be evaluated in parallel. This is usually achieved via sequential maximization of the highly multimodal acquisition function. Unfortunately, this approach parallelizes poorly and is prone to getting stuck in local maxima. Our approach addresses this issue by generating nearly-optimal batches of candidates using an almost-embarrassingly parallel Nested Sampler on the mean prediction of the GP. The resulting nearly-sorted Monte Carlo sample is used to generate a batch of candidates ranked according to their sequentially conditioned acquisition function values at little cost. The final sample can also be used for inferring marginal quantities. Our proposed implementation (NORA) demonstrates comparable accuracy to sequential conditioned acquisition optimization and efficient parallelization in various synthetic and cosmological inference problems.

翻译：贝叶斯推理仍是科学家最重要的工具之一，但日益复杂的实验需要代价更高的似然函数，这增加了生成后验蒙特卡洛样本的成本。近年研究关注基于高斯过程回归的后验模拟器结合主动采样方法，以更少的代价获得相当精度的似然评估。该方法的核心在于对候选点进行批量获取，从而实现真实后验的并行评估。目前通常采用对高度多峰的获取函数进行序贯最大化来实现，但这种方法并行化效果差且易陷入局部最优。本文通过在高斯过程均值预测上应用近乎完美并行的嵌套采样器生成近优候选批次，解决了该问题。由此产生的近排序蒙特卡洛样本被用于生成候选批次，该批次根据其序贯条件获取函数值以较低成本进行排序，最终样本还可用于推断边缘量。所提出的实现方案（NORA）在多种合成与宇宙学推理问题中展现出与序贯条件获取优化相当的精度和高效并行化能力。