本文为新西兰坎特伯雷大学（作者：Andrew Stephen Richens）的硕士论文，共122页。
许多回归问题可以被建模为不相交线段上的独立线性回归。感兴趣的问题是找到线段结束处变化点的数量和位置，以及每个段内的模型阶数。考虑了Fearnhead（2005、2006）提出的一种新方法，这是一种基于模型后验分布的贝叶斯方法。对该算法提出了一些改进：一种选择先验分布参数的方法以及一种消除Fearnhead（2005、2006）中错误源的算法。通过对几种不同模型类型和不同阶数的仿真试验，对该方法进行了分析。然后研究了三个真实的数据集：地质数据、道路安全数据和早产儿医疗数据。尽管在某些情况下会出现错误，但该算法在许多已调查的案例中都被证明是成功的，并且是一种简单有效的发现变化点的方法。
Many regression problems can be modelled asindependent linear regressions on disjoint segments. The problem of interest isto find the number and location of the changepoints where the segments end, andto find the model order inside each segment. A new approach presented inFearnhead (2005, 2006) is considered. This is a Bayesian approach using perfectsimulation from the posterior distribution of the model. Some improvements tothis algorithm are suggested: a method for selecting parameters for the priordistribution used, and an algorithm that eliminates a source of error found inFearnhead (2005, 2006). This method is analysed by testing it on severalsimulations, with different model types and order. Three real datasets are theninvestigated; these are geological data, road safety data and medical data ofpreterm babies. Despite errors in certain situations, the algorithm is shown tobe successful in many of the investigated cases, and an easy and efficient wayof finding changepoints.
- 引言
- 算法
- 仿真
- Well Log数据
- Seat Belt数据
- 婴儿数据
- 结论
附录A Matlab函数结构图
附录B Matlab函数详细列表
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