Quantifying the uncertainty in change points
Quantifying the uncertainty in change points
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DOI：
10.1111/j.1467-9892.2011.00777.x
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发表时间：
2012-09
影响因子：
0.9
通讯作者：
Christopher F. H. Nam;J. Aston;A. M. Johansen
中科院分区：
文献类型：
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作者：
Christopher F. H. Nam;J. Aston;A. M. Johansen
量化时间序列中变化点的位置和性质的不确定性在各种应用中很重要。许多现有的方法，用于估计的数量和位置的变化点不能完全或明确地捕捉这些估计的不确定性，而其他需要显式模拟的大型向量的相关的潜在变量。本文提出了一种方法，用于近似各种变点特征的全后验分布的参数不确定性的存在。该方法结合了最近的工作，通过有限马尔可夫链嵌入在隐马尔可夫模型设置的模型参数的条件下，准确的变化点分布的评估，并通过贝叶斯建模和顺序蒙特卡罗参数的不确定性和估计占。两者的结合导致一个灵活的和计算效率高的过程，这不需要估计的基本状态序列。我们说明，很好的估计后验分布的变化点的特性提供了模拟数据和功能磁共振成像数据。我们使用的方法表明，扫描仪的相关物理特性的建模可以影响检测的变化点和它们的不确定性。
Quantifying the uncertainty in the location and nature of change points in time series is important in a variety of applications. Many existing methods for estimation of the number and location of change points fail to capture fully or explicitly the uncertainty regarding these estimates, whilst others require explicit simulation of large vectors of dependent latent variables. This article proposes methodology for approximating the full posterior distribution of various change point characteristics in the presence of parameter uncertainty. The methodology combines recent work on evaluation of exact change point distributions conditional on model parameters via finite Markov chain imbedding in a hidden Markov model setting, and accounting for parameter uncertainty and estimation via Bayesian modelling and sequential Monte Carlo. The combination of the two leads to a flexible and computationally efficient procedure, which does not require estimates of the underlying state sequence. We illustrate that good estimation of the posterior distributions of change point characteristics is provided for simulated data and functional magnetic resonance imaging data. We use the methodology to show that the modelling of relevant physical properties of the scanner can influence detection of change points and their uncertainty.