基于离散粒子马尔可夫链蒙特卡罗方法的切换状态空间模型贝叶斯推断
Efficient Bayesian Inference for Switching State-Space Models using Discrete Particle Markov Chain Monte Carlo Methods
摘要：
切换状态空间模型（SSSM）是一类非常流行的时间序列模型，在统计学、计量经济学和高级信号处理中有着广泛的应用。这些模型的贝叶斯推断通常依赖于马尔可夫链蒙特卡罗（MCMC）技术。然而，即使是专用于SSSM的复杂MCMC方法也可能被证明是非常低效的，因为它们一次一个地更新潜在的强相关离散值潜变量（Carter和Kohn，1996; Gerlach等人，2000; Giordani和Kohn，2008）。粒子马尔可夫链蒙特卡罗（PMCMC）方法是最近开发的一类MCMC算法，其使用粒子滤波器来构建高维度中的有效建议分布（Andrieu等人，2010年）。Andrieu等人（2010）的现有PMCMC方法适用于SSSM，但限于采用标准粒子滤波技术。然而，在离散值潜变量的背景下，已经开发出了专门的粒子技术，可以超过标准方法一个数量级（Fearnhead，1998; Fearnhead和Clifford，2003; Fearnhead，2004）。在本文中，我们开发了一类新的PMCMC方法依赖于这些非常有效的粒子算法。我们建立了这种新的通用方法称为离散PMCMC的理论有效性，并证明了它的各种例子，包括多个变点模型的测井数据和美国的模型。英国汇率数据。离散PMCMC算法表现出优于实验国家的最先进的MCMC技术为一个固定的计算复杂度。此外，它们可以容易地并行化（Lee等人，2010年），这将带来更大的收益。
英文摘要：
Switching state-space models (SSSM) are a very popular class of time series models that have found many applications in statistics, econometrics and advanced signal processing. Bayesian inference for these models typically relies on Markov chain Monte Carlo (MCMC) techniques. However, even sophisticated MCMC methods dedicated to SSSM can prove quite inefficient as they update potentially strongly correlated discrete-valued latent variables one-at-a-time (Carter and Kohn, 1996; Gerlach et al., 2000; Giordani and Kohn, 2008). Particle Markov chain Monte Carlo (PMCMC) methods are a recently developed class of MCMC algorithms which use particle filters to build efficient proposal distributions in high-dimensions (Andrieu et al., 2010). The existing PMCMC methods of Andrieu et al. (2010) are applicable to SSSM, but are restricted to employing standard particle filtering techniques. Yet, in the context of discrete-valued latent variables, specialised particle techniques have been developed which can outperform by up to an order of magnitude standard methods (Fearnhead, 1998; Fearnhead and Clifford, 2003; Fearnhead, 2004). In this paper we develop a novel class of PMCMC methods relying on these very efficient particle algorithms. We establish the theoretical validy of this new generic methodology referred to as discrete PMCMC and demonstrate it on a variety of examples including a multiple change-points model for well-log data and a model for U.S./U.K. exchange rate data. Discrete PMCMC algorithms are shown to outperform experimentally state-of-the-art MCMC techniques for a fixed computational complexity. Additionally they can be easily parallelized (Lee et al., 2010) which allows further substantial gains.
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