Efficiency of delayed-acceptance random walk Metropolis algorithms
延迟接受随机游走 Metropolis 算法的效率AI 解读 ↓
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延迟接受随机游走 Metropolis 算法的效率
- 研究问题
- 当后验计算昂贵但存在便宜的确定性近似时，如何利用延迟接受机制降低成本，并选择有效的随机游走调参方案？
- 方法与思路
- 作者用便宜近似先筛选提议，再以昂贵计算纠正近似误差；通过高维扩散近似分析常规与伪边际随机游走算法。
- 材料陈述的贡献
- 摘要称，研究给出高维极限效率和接受率表达及调参建议，并用处于极限定理适用域之外的模拟考察稳健性。
- 阅读关注点
- 阅读全文时应核对高维目标与近似误差的条件、效率中的成本定义，以及伪边际噪声和模拟偏离理论条件的方式。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要；适用域外模拟不能替代理论保证，具体调参值及普遍效率优势未说明。
原文摘要
Delayed-acceptance Metropolis–Hastings and delayed-acceptance pseudo-marginal Metropolis–Hastings algorithms can be applied when it is computationally expensive to calculate the true posterior or an unbiased stochastic approximation thereof, but a computationally cheap deterministic approximation is available. An initial accept–reject stage uses the cheap approximation for computing the Metropolis–Hastings ratio; proposals which are accepted at this stage are subjected to a further accept–reject step, which corrects for the error in the approximation. Since the expensive posterior, or the approximation thereof, is only evaluated for proposals which are accepted at the first stage, the cost of the algorithm is reduced and larger scalings may be used. We focus on the random walk Metropolis (RWM) and consider the delayed-acceptance RWM and the delayed-acceptance pseudo-marginal RWM. We provide a framework for incorporating relatively general deterministic approximations into the theoretical analysis of high-dimensional targets. Justified by diffusion-approximation arguments, we derive expressions for the limiting efficiency and acceptance rates in high-dimensional settings. Finally, these theoretical insights are leveraged to formulate practical guidelines for the efficient tuning of the algorithms. The robustness of these guidelines and predicted properties are verified against simulation studies, all of which are strictly outside of the domain of validity of our limit results.