Functional data registration is a necessary processing step for many applications. The observed data can be inherently noisy, often due to measurement error or natural process uncertainty, which most functional alignment methods cannot handle. A pair of functions can also have multiple optimal alignment solutions, which is not addressed in current literature. In this paper, a flexible Bayesian approach to functional alignment is presented, which appropriately accounts for noise in the data without any pre-smoothing required. Additionally, by running parallel MCMC chains, the method can account for multiple optimal alignments via the multi-modal posterior distribution of the warping functions. To most efficiently sample the warping functions, the approach relies on a modification of the standard Hamiltonian Monte Carlo to be well-defined on the infinite-dimensional Hilbert space. This flexible Bayesian alignment method is applied to both simulated data and real data sets to show its efficiency in handling noisy functions and successfully accounting for multiple optimal alignments in the posterior; characterizing the uncertainty surrounding the warping functions.
翻译:功能数据登记是许多应用中一个必要的处理步骤。 观察到的数据本身可能很吵, 通常是由于测量错误或自然过程不确定性, 而大多数功能对齐方法都无法处理。 一对功能还可以有多重最佳的对齐解决方案, 而当前的文献对此没有涉及。 本文介绍了一种灵活的贝叶斯人功能对齐方法, 该方法在无需事先抽动的情况下适当记录数据中的噪音。 此外, 通过运行平行的 MCMC 链, 该方法可以通过扭曲函数的多式后端分布来核算多个最佳对齐。 为了最高效地取样扭曲函数, 该方法依赖于对汉密尔顿·蒙特·卡洛标准进行修改,以便在无限维度的希尔伯特空间上进行明确界定。 这种灵活的贝斯人对齐方法既适用于模拟数据,也适用于真实的数据集, 以显示其处理扰动功能的效率, 也能够成功计算后端函数中多个最佳的对齐值; 描述扭曲功能的不确定性。