标题： 状态空间模型中参数推断的耦合随机EM和近似贝叶斯计算 显示英文标题

标题： Coupling stochastic EM and Approximate Bayesian Computation for parameter inference in state-space models

摘要： 我们研究状态空间模型类，并对模型参数进行最大似然估计。 我们考虑一种随机近似期望最大化（SAEM）算法，以在SAEM中使用近似贝叶斯计算（ABC）来最大化似然函数，这是其创新之处。 任务是为SAEM的每次迭代提供系统的过滤状态，这通过基于序贯蒙特卡洛（SMC）方法的ABC采样器来实现。 结果表明，所得的SAEM-ABC算法可以校准以返回准确的推断，在某些情况下它可以优于包含Bootstrap滤波器的SAEM版本。 展示了两个模拟研究，首先是非线性高斯状态空间模型，然后是动态由随机微分方程表达的状态空间模型。 给出了与用于最大似然推断的迭代过滤方法，以及用于贝叶斯推断的Gibbs抽样和粒子边际方法的比较。 显示英文摘要

摘要： We study the class of state-space models and perform maximum likelihood estimation for the model parameters. We consider a stochastic approximation expectation-maximization (SAEM) algorithm to maximize the likelihood function with the novelty of using approximate Bayesian computation (ABC) within SAEM. The task is to provide each iteration of SAEM with a filtered state of the system, and this is achieved using an ABC sampler for the hidden state, based on sequential Monte Carlo (SMC) methodology. It is shown that the resulting SAEM-ABC algorithm can be calibrated to return accurate inference, and in some situations it can outperform a version of SAEM incorporating the bootstrap filter. Two simulation studies are presented, first a nonlinear Gaussian state-space model then a state-space model having dynamics expressed by a stochastic differential equation. Comparisons with iterated filtering for maximum likelihood inference, and Gibbs sampling and particle marginal methods for Bayesian inference are presented.