用多精度模拟加速马尔可夫链蒙特卡洛，提升采样效率。
FLARE MCMC: Fidelity-based Layer-Adaptive REcursive proposals for MCMC
- 通过分层递归链使用低精度近似似然函数加速采样
- 相同计算时间下有效样本量显著提升，跨水文与宇宙学领域验证
- 无需似然函数特定形式，适用于模拟可调精度的科学模型
马尔可夫链蒙特卡洛（MCMC）仅需评估似然函数，是复杂模型推断的常用方法。但其混合速率慢，需生成大量样本才能获得良好估计，整体计算成本高。FLARE MCMC 是一种多保真度分层 MCMC 方法，利用真实似然函数的低保真度近似来改善混合速度，从而实现整体更快性能。此类低保真度似然在科学与工程应用中常见，因模型涉及可调节分辨率或精度的模拟。本方法采用递归分层链和简单层调优策略，无需似然函数具有特定形式或内部数学结构。实验表明，FLARE MCMC 在水文与宇宙学等多个科学领域中，于相同计算时间内实现了更大的有效样本量。
原文摘要 · Abstract (English)
Markov chain Monte Carlo (MCMC) requires only the ability to evaluate the likelihood, making it a common technique for inference in complex models. However, it can have a slow mixing rate, requiring the generation of many samples to obtain good estimates and an overall high computational cost. FLARE MCMC is a multi-fidelity layered MCMC method that exploits lower-fidelity approximations of the true likelihood calculation to improve mixing and leads to overall faster performance. Such lower-fidelity likelihoods are commonly available in scientific and engineering applications where the model involves a simulation whose resolution or accuracy can be tuned. Our technique uses recursive, layered chains with simple layer tuning; it does not require the likelihood to take any form or have any particular internal mathematical structure. We demonstrate experimentally that FLARE MCMC achieves larger effective sample sizes for the same computational time across different scientific domains including hydrology and cosmology.
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