Single chain differential evolution Monte-Carlo for self-tuning Bayesian inference
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用于自调节贝叶斯推断的单链差分进化蒙特卡洛
- 研究问题
- 如何将依赖多条链当前位置的差分进化蒙特卡洛改为单链采样，保留自调节能力并减少昂贵模型的后验计算负担？
- 方法与思路
- 作者利用单条链历史状态之差构造采样步骤，每步只需一次后验评价，并在二元正态和人工捕食者—猎物 ODE 模型中比较方法。
- 材料陈述的贡献
- 摘要称，两项案例中单链 DEMC 与自适应 MCMC 的后验估计精度相当，运行更快、有效样本量更高且初始样本自相关更低。
- 阅读关注点
- 应核对历史状态抽取与接受规则、自适应采样的有效性条件，以及运行时间、有效样本量和精度比较采用的计算预算与设置。
- 阅读边界
- 这是 arXiv 预印本，同行评审或期刊接收未经核实。速度与精度结论来自两个案例，摘要未提供普遍收敛条件或广泛基准证据。
原文摘要
1. Bayesian inference is difficult because it often requires time consuming tuning of samplers. Differential evolution Monte-Carlo (DEMC) is a self-tuning multi-chain sampling approach which requires minimal input from the operator as samples are obtained by taking the difference of the current position of multiple randomly selected chains. However, this can also make DEMC more computationally intensive than single chain samplers. 2. We provide a single-chain adaptation of the DEMC algorithm by taking samples according to the difference in previous states of the chain, rather than the current state of multiple chains. This minimises computational costs by requiring only one posterior evaluation per step, while retaining the self-adaptive property of DEMC. We test the algorithm by sampling a bivariate normal distribution and by estimating the posterior distribution of parameters of an ODE model fitted to an artificial prey-predator time series. In both cases we compare the quality of DEMC generated samples to those obtained by a standard adaptive Markov chain Monte-Carlo sampler (AMC). 3. In both case studies, DEMC is as accurate as AMC in estimating posterior distributions, while being an order of magnitude faster due to simpler computations. DEMC also provides a higher effective samples size than AMC, and lower initial samples autocorrelations. 4. Its low computational cost and self-adaptive property make single chain DEMC particularly suitable for fitting models that are costly to evaluate, such as ODE models. The simplicity of the algorithm also makes it easy to implement in base R, hence offering a simple alternative to STAN.