论文标题
单链差分进化蒙特卡洛用于自我调整的贝叶斯推断
Single chain differential evolution Monte-Carlo for self-tuning Bayesian inference
论文作者
论文摘要
1。贝叶斯推断很困难，因为它通常需要耗时的采样器调整。差异进化蒙特卡洛（DEMC）是一种自我调整的多链采样方法，需要从操作员那里获得最小的输入，因为取得样本是通过取用多个随机选择链的当前位置的差异来获得的。但是，这也可以使DEMC比单链采样器更加强大。 2。我们通过根据链的先前状态而不是当前多个链的当前状态采集样品来提供DEMC算法的单链适应。这可以通过每步仅需要一个后验评估来最大程度地减少计算成本，同时保留DEMC的自适应性能。我们通过对双变量正态分布进行采样并估算拟合到人工猎物预言时间序列的ode模型的参数的后验分布来测试算法。在这两种情况下，我们都将DEMC生成的样品的质量与标准自适应马尔可夫链蒙特卡洛采样器（AMC）获得的样品进行了比较。 3。在两种案例研究中，DEMC在估计后验分布时与AMC一样准确，而由于更简单的计算，demC是更快的数量级。 DEMC还提供了比AMC更高的有效样品大小，并且初始样品自相关性较低。 4。其低计算成本和自适应属性使单链DEMC特别适合拟合昂贵的评估模型，例如ODE模型。该算法的简单性也使在基本R中实现变得易于实现，因此提供了Stan的简单替代方案。
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.
