Ensemble MCMC: Accelerating Pseudo-Marginal MCMC for State Space Models using the Ensemble Kalman Filter
Ensemble MCMC: Accelerating Pseudo-Marginal MCMC for State Space Models using the Ensemble Kalman Filter
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DOI：
10.1214/20-ba1251
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发表时间：
2019-06
影响因子：
4.4
通讯作者：
C. Drovandi;R. Everitt;A. Golightly;D. Prangle
中科院分区：
文献类型：
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作者：
C. Drovandi;R. Everitt;A. Golightly;D. Prangle
粒子马尔可夫链蒙特卡罗（pMCMC）是一种流行的方法，用于对具有未知静态参数的具有挑战性的状态空间模型（SSM）进行贝叶斯统计推断。它在MCMC算法的每次迭代中使用粒子滤波器（PF）来无偏地估计给定静态参数值的可能性。然而，当PF中需要大量颗粒时，例如当数据信息量很大、模型被错误指定和/或时间序列很长时，pMCMC可能是计算密集型的。在本文中，我们利用集合卡尔曼滤波（EnKF）的数据同化文献中开发的pMCMC加速。我们用MCMC中的有偏EnKF似然估计代替无偏PF似然估计，在静态参数的空间上进行采样。在广泛的一类不同的非线性SSM模型，我们证明了我们的新的合奏MCMC（eMCMC）方法可以显着降低计算成本，同时保持合理的精度。我们还提出了几个扩展的香草eMCMC算法，以进一步提高计算效率。在所有示例中实现我们方法的计算机代码可以从这个https URL下载。
Particle Markov chain Monte Carlo (pMCMC) is now a popular method for performing Bayesian statistical inference on challenging state space models (SSMs) with unknown static parameters. It uses a particle filter (PF) at each iteration of an MCMC algorithm to unbiasedly estimate the likelihood for a given static parameter value. However, pMCMC can be computationally intensive when a large number of particles in the PF is required, such as when the data is highly informative, the model is misspecified and/or the time series is long. In this paper we exploit the ensemble Kalman filter (EnKF) developed in the data assimilation literature to speed up pMCMC. We replace the unbiased PF likelihood with the biased EnKF likelihood estimate within MCMC to sample over the space of the static parameter. On a wide class of different non-linear SSM models, we demonstrate that our new ensemble MCMC (eMCMC) method can significantly reduce the computational cost whilst maintaining reasonable accuracy. We also propose several extensions of the vanilla eMCMC algorithm to further improve computational efficiency. Computer code to implement our methods on all the examples can be downloaded from this https URL.