Time-Series Filtering for Replicated Observations via a Kernel Approximate Bayesian Computation
Time-Series Filtering for Replicated Observations via a Kernel Approximate Bayesian Computation
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DOI：
10.1109/tsp.2018.2872864
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发表时间：
2018-12
影响因子：
5.4
通讯作者：
Takanori Hasegawa;Kaname Kojima;Y. Kawai;Masao Nagasaki
中科院分区：
文献类型：
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作者：
Takanori Hasegawa;Kaname Kojima;Y. Kawai;Masao Nagasaki
在时间序列分析中，状态空间模型（SSM）已被广泛用于估计隐藏变量和参数值的条件概率分布，以及理解可以生成数据的结构。例如，卡尔曼滤波器用于分析计算线性 SSM 上的条件概率分布，以最小化方差，并且一些扩展（例如无迹卡尔曼滤波器和粒子滤波器）已应用于计算非线性 SSM 的近似分布。最近，近似贝叶斯计算（ABC）已被应用于此类时间序列过滤，以处理棘手的可能性；然而，在持续减少估计偏差、评估模型的有效性以及处理重复观察方面仍然存在问题。为了解决这些问题，本文提出了一种结合内核 ABC 的新方法，在 SSM 中执行滤波、参数估计和模型评估。仿真研究表明，所提出的方法产生的推论与其他 ABC 方法相当，优点是不需要仔细校准 ABC 阈值。此外，我们还使用来自非线性 SSM 的合成数据的真实且有竞争力的模型来评估模型选择能力的性能。最后，我们将所提出的方法应用于大鼠昼夜节律振荡的真实数据，并证明了其在实际情况中的有用性。
In time-series analysis, state-space models (SSMs) have been widely used to estimate the conditional probability distributions of hidden variables and parameter values, as well as to understand structures that can generate the data. For example, the Kalman filter is used to analytically calculate the conditional probability distribution on linear SSMs in terms of minimizing the variance, and several extensions, such as the unscented Kalman filter and particle filter, have been applied to calculate the approximate distribution on nonlinear SSMs. Recently, the approximate Bayesian computation (ABC) has been applied to such time-series filtering to handle intractable likelihoods; however, it remains problematic with respect to consistently achieving a reduction of the estimation bias, evaluating the validity of the models, and dealing with replicated observations. To address these problems, in this paper, we propose a novel method combined with the kernel ABC to perform filtering, parameter estimation, and the model evaluation in SSMs. Simulation studies show that the proposed method produces inference that is comparable to other ABC methods, with the advantage of not requiring a careful calibration of the ABC threshold. In addition, we evaluate the performance of the model-selection capability using true and competitive models on synthetic data from nonlinear SSMs. Finally, we apply the proposed method to real data in rat circadian oscillations, and demonstrated the usefulness in practical situations.