Nested particle filters for online parameter estimation in discrete-time state-space Markov models
Nested particle filters for online parameter estimation in discrete-time state-space Markov models
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DOI：
10.3150/17-bej954
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发表时间：
2018-11-01
期刊：
影响因子：
1.5
通讯作者：
Miguez, Joaquin
中科院分区：
文献类型：
--
作者：
Crisan, Dan;Miguez, Joaquin
我们解决的问题，近似的后验概率分布的状态空间动力系统的固定参数使用顺序蒙特卡罗方法。所提出的方法依赖于一个嵌套的结构，采用两层粒子滤波器近似的静态参数和动态状态变量的系统的后验概率测量的兴趣，静脉类似于最近的“顺序蒙特卡罗平方”（SMC 2）算法。然而，与SMC 2方案不同，所提出的技术以纯递归方式操作。特别地，本文介绍的方法的递归步骤的计算复杂度随时间恒定。我们分析了真实的有界函数的积分关于通过所提出的计划计算的系统参数的后验分布的逼近。结果证明，在正则性假设下，逼近误差在L-p（p >= 1）中渐近消失，收敛速度与1/root N + 1/root M成正比，其中N是参数空间中的Monte Carlo样本数，N × M是状态空间中的样本数.这一结果也适用于参数和状态变量的联合后验分布的近似。我们讨论了SMC 2算法和新的递归方法之间的关系，并给出了一个简单的例子，以便通过计算机模拟来说明一些理论发现。
We address the problem of approximating the posterior probability distribution of the fixed parameters of a state-space dynamical system using a sequential Monte Carlo method. The proposed approach relies on a nested structure that employs two layers of particle filters to approximate the posterior probability measure of the static parameters and the dynamic state variables of the system of interest, in a vein similar to the recent "sequential Monte Carlo square" (SMC2) algorithm. However, unlike the SMC2 scheme, the proposed technique operates in a purely recursive manner. In particular, the computational complexity of the recursive steps of the method introduced herein is constant over time. We analyse the approximation of integrals of real bounded functions with respect to the posterior distribution of the system parameters computed via the proposed scheme. As a result, we prove, under regularity assumptions, that the approximation errors vanish asymptotically in L-p (p >= 1) with convergence rate proportional to 1/root N + 1/root M, where N is the number of Monte Carlo samples in the parameter space and N x M is the number of samples in the state space. This result also holds for the approximation of the joint posterior distribution of the parameters and the state variables. We discuss the relationship between the SMC2 algorithm and the new recursive method and present a simple example in order to illustrate some of the theoretical findings with computer simulations.