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首页> 外文期刊>Journal of applied statistics >Generalized bent-cable methodology for changepoint data: a Bayesian approach
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Generalized bent-cable methodology for changepoint data: a Bayesian approach

机译：变更点数据的通用弯曲电缆方法：贝叶斯方法

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摘要

The choice of the model framework in a regression setting depends on the nature of the data. The focus of this study is on changepoint data, exhibiting three phases: incoming and outgoing, both of which are linear, joined by a curved transition. Bent-cable regression is an appealing statistical tool to characterize such trajectories, quantifying the nature of the transition between the two linear phases by modeling the transition as a quadratic phase with unknown width. We demonstrate that a quadratic function may not be appropriate to adequately describe many changepoint data. We then propose a generalization of the bent-cable model by relaxing the assumption of the quadratic bend. The properties of the generalized model are discussed and a Bayesian approach for inference is proposed. The generalized model is demonstrated with applications to three data sets taken from environmental science and economics. We also consider a comparison among the quadratic bent-cable, generalized bent-cable and piecewise linear models in terms of goodness of fit in analyzing both real-world and simulated data. This study suggests that the proposed generalization of the bent-cable model can be valuable in adequately describing changepoint data that exhibit either an abrupt or gradual transition over time.
机译：在回归设置中对模型框架的选择取决于数据的性质。这项研究的重点是变更点数据，它表现为三个阶段：输入和输出都是线性的，并通过弯曲的过渡连接在一起。弯曲电缆回归是一种吸引人的统计工具，用于表征此类轨迹，通过将过渡建模为宽度未知的二次相来量化两个线性相之间过渡的性质。我们证明，二次函数可能不适用于充分描述许多变化点数据。然后，我们通过放宽二次弯曲的假设来提出弯曲电缆模型的一般化。讨论了广义模型的性质，并提出了贝叶斯推理方法。通过将其应用于从环境科学和经济学中获得的三个数据集，证明了该通用模型。我们还考虑了在分析实际数据和模拟数据时的拟合优度方面，对二次弯曲电缆，广义弯曲电缆和分段线性模型之间的比较。这项研究表明，对弯曲电缆模型的拟议推广对于充分描述随时间而变化或突然变化的变化点数据可能是有价值的。

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