arXiv 1809.025272018-09-07stat.ME

状态空间模型的可扩展蒙特卡罗推断

Scalable Monte Carlo inference for state-space models

Sinan Yıldırım, Christophe Andrieu, Arnaud Doucet

摘要：

我们提出了一个原始的基于模拟的方法来估计一般状态空间模型的似然比有效。我们的方法依赖于一个新的使用条件序贯蒙特卡罗（cSMC）算法引入\citet{Andrieu_et_al_2010}，并提出了一些实际的优势，标准的方法。该比率是使用唯一的随机性源估计的，而不是分别估计所涉及的两个似然项。除了方差减小方面的好处之外，人们通常可以从这种类型的方法中期望，这里的重要一点是，该估计量的方差随着似然参数之间的距离减小而减小。我们将展示如何利用这一点的背景下，蒙特卡罗马尔可夫链（MCMC）算法，导致一类新的精确近似MCMC方法的发展进行贝叶斯静态参数推断的状态空间模型。我们通过模拟表明，与Andrieu_et_al_2010年的粒子边际大都市黑斯廷斯（PMMH）算法相比，这种新的MCMC方案所需的计算工作量非常有利于大数据集的扩展。

英文摘要：

We present an original simulation-based method to estimate likelihood ratios efficiently for general state-space models. Our method relies on a novel use of the conditional Sequential Monte Carlo (cSMC) algorithm introduced in \citet{Andrieu_et_al_2010} and presents several practical advantages over standard approaches. The ratio is estimated using a unique source of randomness instead of estimating separately the two likelihood terms involved. Beyond the benefits in terms of variance reduction one may expect in general from this type of approach, an important point here is that the variance of this estimator decreases as the distance between the likelihood parameters decreases. We show how this can be exploited in the context of Monte Carlo Markov chain (MCMC) algorithms, leading to the development of a new class of exact-approximate MCMC methods to perform Bayesian static parameter inference in state-space models. We show through simulations that, in contrast to the Particle Marginal Metropolis-Hastings (PMMH) algorithm of Andrieu_et_al_2010, the computational effort required by this novel MCMC scheme scales very favourably for large data sets.

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