A BAYESIAN-ANALYSIS FOR CHANGE POINT PROBLEMS
A BAYESIAN-ANALYSIS FOR CHANGE POINT PROBLEMS
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DOI：
10.1080/01621459.1993.10594323
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发表时间：
1993-03-01
影响因子：
3.7
通讯作者：
HARTIGAN, JA
中科院分区：
文献类型：
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作者：
BARRY, D;HARTIGAN, JA
一系列的观测在未知的时间发生突变。我们建模的过程中，假设有一个基本的参数序列划分成连续的块相等的参数值，每个块的开始被称为是一个变化点。然后假设观测在给定参数序列的不同块中是独立的。在贝叶斯分析中，有必要给出变点和参数的概率分布。我们使用乘积分割模型（巴里和哈蒂根，1992），它假设任何分割的概率与先验内聚性的乘积成比例，分割中的每个块对应一个内聚性，并且给定块，不同块中的参数具有独立的先验分布。给定观察结果，新的产品划分模型保持不变，具有块的后验凝聚力和新的独立块参数后验分布。因此，乘积模型提供了一种方便的机制，允许数据对可能保持的分区进行加权;然后可以通过首先对分区进行调节，然后对所有分区进行平均来推断特定参数。参数值可以在O（n3）计算中精确估计，或者通过马尔可夫抽样技术在观测次数上为O（n）的适当近似。因此，马尔可夫抽样计算是可行的长序列。我们比较这个模型与一些替代方法来拟合变化点和参数时，误差分布是正常的，然后表明，所提出的方法是上级替代品在检测急剧的短暂变化的参数。
A sequence of observations undergoes sudden changes at unknown times. We model the process by supposing that there is an underlying sequence of parameters partitioned into contiguous blocks of equal parameter values; the beginning of each block is said to be a change point. Observations are then assumed to be independent in different blocks given the sequence of parameters. In a Bayesian analysis it is necessary to give probability distributions to both the change points and the parameters. We use product partition models (Barry and Hartigan 1992), which assume that the probability of any partition is proportional to a product of prior cohesions, one for each block in the partition, and that given the blocks the parameters in different blocks have independent prior distributions. Given the observations a new product partition model holds, with posterior cohesions for the blocks and new independent block posterior distributions for parameters. The product model thus provides a convenient machinery for allowing the data to weight the partitions likely to hold; inference about particular parameters may then be made by first conditioning on the partition, and then averaging over all partitions. The parameter values may be estimated exactly in O(n3) calculations, or to an adequate approximation by Markov sampling techniques that are O(n) in the number of observations. The Markov sampling computations are thus practicable for long sequences. We compare this model with a number of altemative approaches to fitting change points and parameters when the error distribution is normal, then show that the proposed method is superior to the alternatives in detecting sharp short-lived changes in the parameters.