Sequential Bayesian inference for implicit hidden Markov models and current limitations
Sequential Bayesian inference for implicit hidden Markov models and current limitations
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DOI：
10.1051/proc/201551002
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发表时间：
2015-05
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影响因子：
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通讯作者：
P. Jacob
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文献类型：
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作者：
P. Jacob
隐马尔可夫模型可以通过将数据视为任意复杂马尔可夫过程的噪声测量来描述各个科学领域中出现的时间序列。顺序蒙特卡罗 (SMC) 方法已成为在给定观测值和固定参数值的情况下估计隐马尔可夫过程的标准工具。我们回顾了一些最近的进展，允许包含参数不确定性以及模型不确定性。从算法复杂性的角度强调了当前可用方法的缺点。时间序列分析感兴趣的统计对象在人口生态学中使用的玩具“Lotka-Volterra”模型上进行了说明。讨论了一些关于所审查方法对更长时间序列、更高维状态空间和更灵活模型的可扩展性的开放挑战。
Hidden Markov models can describe time series arising in various fields of science, by treating the data as noisy measurements of an arbitrarily complex Markov process. Sequential Monte Carlo (SMC) methods have become standard tools to estimate the hidden Markov process given the observations and a fixed parameter value. We review some of the recent developments allowing the inclusion of parameter uncertainty as well as model uncertainty. The shortcomings of the currently available methodology are emphasised from an algorithmic complexity perspective. The statistical objects of interest for time series analysis are illustrated on a toy "Lotka-Volterra" model used in population ecology. Some open challenges are discussed regarding the scalability of the reviewed methodology to longer time series, higher-dimensional state spaces and more flexible models.