连续时间随机模型的贝叶斯多变化点检测

IF 4.9 2区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Bayesian Analysis Pub Date : 2021-06-01 DOI:10.1214/20-ba1218
Lu Shaochuan
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引用次数: 6

摘要

将连续时间下的多变点模型表述为定义在可数无限状态空间上的连续时间隐马尔可夫模型。多更改点模型的新公式允许模型复杂性,即更改点的数量,在新数据到达时无限制地累积。对变化点的数量及其位置的推断是基于一个折叠的吉布斯采样器。我们提出了一种新的连续时间前向滤波后向采样(FFBS)算法,用于模拟潜在马尔可夫链(即变化点)的完整轨迹。FFBS算法通过均匀化方案对潜在马尔可夫链进行随机时间离散化,并结合离散时间版本的FFBS算法。结果表明,FFBS算法的计算成本和内存成本都仅是变化点数量的二次元。多变化点模型的新公式允许变化尺度的变化点运行长度的特征。通过模拟和实际地震数据实例对方法进行了验证。
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Bayesian Multiple Changepoint Detection for Stochastic Models in Continuous Time
A multiple changepoint model in continuous time is formulated as a continuous-time hidden Markov model, defined on a countable infinite state space. The new formulation of the multiple changepoint model allows the model complexities, i.e. the number of changepoints, to accrue unboundedly upon the arrivals of new data. Inference on the number of changepoints and their locations is based on a collapsed Gibbs sampler. We suggest a new version of forward-filtering backward-sampling (FFBS) algorithm in continuous time for simulating the full trajectory of the latent Markov chain, i.e. the changepoints. The FFBS algorithm is based on a randomized time-discretization for the latent Markov chain through uniformization schemes, combined with a discrete-time version of FFBS algorithm. It is shown that, desirably, both the computational cost and the memory cost of the FFBS algorithm are only quadratic to the number of changepoints. The new formulation of the multiple changepoint models allows varying scale of run lengths of changepoints to be characterized. We demonstrate the methods through simulations and a real data example for earthquakes.
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来源期刊
Bayesian Analysis
Bayesian Analysis 数学-数学跨学科应用
CiteScore
6.50
自引率
13.60%
发文量
59
审稿时长
>12 weeks
期刊介绍: Bayesian Analysis is an electronic journal of the International Society for Bayesian Analysis. It seeks to publish a wide range of articles that demonstrate or discuss Bayesian methods in some theoretical or applied context. The journal welcomes submissions involving presentation of new computational and statistical methods; critical reviews and discussions of existing approaches; historical perspectives; description of important scientific or policy application areas; case studies; and methods for experimental design, data collection, data sharing, or data mining. Evaluation of submissions is based on importance of content and effectiveness of communication. Discussion papers are typically chosen by the Editor in Chief, or suggested by an Editor, among the regular submissions. In addition, the Journal encourages individual authors to submit manuscripts for consideration as discussion papers.
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