Bayesian Framework for Simultaneous Registration and Estimation of Noisy, Sparse, and Fragmented Functional Data
Bayesian Framework for Simultaneous Registration and Estimation of Noisy, Sparse, and Fragmented Functional Data
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DOI：
10.1080/01621459.2021.1893179
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发表时间：
2021-03-25
影响因子：
3.7
通讯作者：
Kurtek, Sebastian
中科院分区：
文献类型：
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作者：
Matuk, James;Bharath, Karthik;Kurtek, Sebastian
在许多应用中，平滑过程产生的数据是在各种观测制度下记录的，包括密集采样和稀疏或碎片化的观测，这些观测经常受到误差的污染。到目前为止，从离散观测中登记和估计单个潜在函数的统计目标主要是在没有正式不确定性传播的情况下顺序实现的，或者通过跨主题汇集信息以特定应用的方式实现。我们提出了一个统一的贝叶斯框架，用于同时配准和估计，该框架足够灵活，可以适应一般观测制度下对单个函数的推断。我们做到这一点的能力依赖于使用两种策略对函数变异性的振幅分量的强信息先验模型的规范：一种数据驱动的方法，基于训练数据定义振幅子空间的经验基础，以及一种形状限制的方法，当极值的相对位置和数量被很好地理解时。该方法建立在弹性功能数据分析框架的基础上，分别对功能数据中固有的幅度和相位变异性进行建模。我们强调这两个组成部分的不确定性量化和可视化的重要性，因为它们提供了关于估计函数的补充信息。我们通过多个仿真研究和实际应用验证了所提出的框架。
In many applications, smooth processes generate data that are recorded under a variety of observational regimes, including dense sampling and sparse or fragmented observations that are often contaminated with error. The statistical goal of registering and estimating the individual underlying functions from discrete observations has thus far been mainly approached sequentially without formal uncertainty propagation, or in an application-specific manner by pooling information across subjects. We propose a unified Bayesian framework for simultaneous registration and estimation, which is flexible enough to accommodate inference on individual functions under general observational regimes. Our ability to do this relies on the specification of strongly informative prior models over the amplitude component of function variability using two strategies: a data-driven approach that defines an empirical basis for the amplitude subspace based on training data, and a shape-restricted approach when the relative location and number of extrema is well-understood. The proposed methods build on the elastic functional data analysis framework to separately model amplitude and phase variability inherent in functional data. We emphasize the importance of uncertainty quantification and visualization of these two components as they provide complementary information about the estimated functions. We validate the proposed framework using multiple simulation studies and real applications.