A geometric approach to pairwise Bayesian alignment of functional data using importance sampling
A geometric approach to pairwise Bayesian alignment of functional data using importance sampling
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DOI：
10.1214/17-ejs1243
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发表时间：
2017-01-01
影响因子：
1.1
通讯作者：
Kurtek, Sebastian
中科院分区：
文献类型：
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作者：
Kurtek, Sebastian
我们提出了函数数据的两两非线性配准的贝叶斯模型。我们利用翘曲函数空间的黎曼几何来定义适当的先验分布，并使用重要性抽样从后验抽样。使用简单的平方根变换来简化翘曲函数空间的几何形状，这允许计算样本统计量，如平均值和中位数，并快速实现k-均值聚类算法。这些工具允许有效的后验推断，其中找到了对应于给定函数的多个看似合理的对齐的后验分布的多种模式。我们还给出了逐点95%的可信区间来评估不同集群中比对的不确定性。我们通过仿真对该模型进行了验证，并在生物特征识别和医学等不同应用领域的真实数据上给出了多个例子。
We present a Bayesian model for pairwise nonlinear registration of functional data. We use the Riemannian geometry of the space of warping functions to define appropriate prior distributions and sample from the posterior using importance sampling. A simple square-root transformation is used to simplify the geometry of the space of warping functions, which allows for computation of sample statistics, such as the mean and median, and a fast implementation of a k-means clustering algorithm. These tools allow for efficient posterior inference, where multiple modes of the posterior distribution corresponding to multiple plausible alignments of the given functions are found. We also show pointwise 95% credible intervals to assess the uncertainty of the alignment in different clusters. We validate this model using simulations and present multiple examples on real data from different application domains including biometrics and medicine.