标题： 贝叶斯变点检测用于函数型数据 显示英文标题

标题： Bayesian Change Point Detection for Functional Data

摘要： 我们提出了一种贝叶斯方法来检测函数数据中的变化点。 我们通过离散小波变换（DWT）提取函数数据序列的特征，并独立处理每个特征序列。 我们认为每个特征在可能不同的时间点上可能存在变化。 函数数据通过这些变化在整个观测序列中演变。 该函数数据序列的变化点是所有特征变化的累积效应。 我们为特征分配了先验，这些先验包含了小波系数的特性。 然后我们计算每个特征序列的变化点后验分布，并定义一个矩阵，其中每个元素是该序列中两个函数数据之间相似性的度量。 我们计算所有可能划分中组间平均相似性和组内平均相似性的比率，变化点即为该比率最小的位置。 我们使用气候变化的数据集演示了这种方法。 显示英文摘要

摘要： We propose a Bayesian method to detect change points for functional data. We extract the features of a sequence of functional data by the discrete wavelet transform (DWT), and treat each sequence of feature independently. We believe there is potentially a change in each feature at possibly different time points. The functional data evolves through such changes throughout the sequences of observations. The change point for this sequence of functional data is the cumulative effect of changes in all features. We assign the features with priors which incorporate the characteristic of the wavelet coefficients. Then we compute the posterior distribution of change point for each sequence of feature, and define a matrix where each entry is a measure of similarity between two functional data in this sequence. We compute the ratio of the mean similarity between groups and within groups for all possible partitions, and the change point is where the ratio reaches the minimum. We demonstrate this method using a dataset on climate change.