嵌入隐马尔可夫模型与粒子马尔可夫链蒙特卡罗方法
On embedded hidden Markov models and particle Markov chain Monte Carlo methods
摘要：
嵌入式隐马尔可夫模型（EHMM）采样方法是一种用于非线性非高斯状态空间模型中状态推断的马尔可夫链蒙特卡罗（MCMC）技术，由Neal（2003）提出; Neal et al.（2004）和Shestopaloff and Neal（2016）扩展。Shestopaloff和Neal（2013）提出了对贝叶斯参数推断的扩展。粒子MCMC（PMCMC）方法提供了另一类解决类似推理问题的MCMC方案（Andrieu et al. 2009; 2010）。所有这些方法都依赖于引入多个状态序列的人工扩展目标分布，通过构造，这些状态序列是这样的，即根据感兴趣的后验分布一个随机索引的序列。通过将PMCMC方法框架下的梅特罗波利斯-黑斯廷斯算法应用于EHMM框架，得到了新的粒子滤波器（PF）型状态推断算法和新的MCMC参数和状态推断算法.此外，我们表明，这些算法中的大多数可以被视为一般PF和PMCMC框架的特殊情况。我们比较了各种算法在低维到高维状态空间模型上的经验性能。我们证明了Shestopaloff和Neal（2016）提出的具有“局部”MCMC移动的适当调整的条件PF在应用于高维状态空间模型时可以显着优于标准条件PF，而新的PF类型算法可以证明是标准PF的一个有趣的替代方案，用于某些低维场景中的似然估计。
英文摘要：
The embedded hidden Markov model (EHMM) sampling method is a Markov chain Monte Carlo (MCMC) technique for state inference in non-linear non-Gaussian state-space models which was proposed in Neal (2003); Neal et al. (2004) and extended in Shestopaloff and Neal (2016). An extension to Bayesian parameter inference was presented in Shestopaloff and Neal (2013). An alternative class of MCMC schemes addressing similar inference problems is provided by particle MCMC (PMCMC) methods (Andrieu et al. 2009; 2010). All these methods rely on the introduction of artificial extended target distributions for multiple state sequences which, by construction, are such that one randomly indexed sequence is distributed according to the posterior of interest. By adapting the Metropolis-Hastings algorithms developed in the framework of PMCMC methods to the EHMM framework, we obtain novel particle filter (PF)-type algorithms for state inference and novel MCMC schemes for parameter and state inference. In addition, we show that most of these algorithms can be viewed as particular cases of a general PF and PMCMC framework. We compare the empirical performance of the various algorithms on low- to high-dimensional state-space models. We demonstrate that a properly tuned conditional PF with "local" MCMC moves proposed in Shestopaloff and Neal (2016) can outperform the standard conditional PF significantly when applied to high-dimensional state-space models while the novel PF-type algorithm could prove to be an interesting alternative to standard PFs for likelihood estimation in some lower-dimensional scenarios.
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