Bayesian Registration of Functions and Curves
Bayesian Registration of Functions and Curves
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DOI：
10.1214/15-ba957
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发表时间：
2016-06-01
影响因子：
4.4
通讯作者：
Huang, Xianzheng
中科院分区：
文献类型：
--
作者：
Cheng, Wen;Dryden, Ian L.;Huang, Xianzheng
考虑函数和曲线的贝叶斯分析，其中通常需要翘曲和其他几何变换来进行有意义的比较。使用最近引入的平方根速度函数来表示感兴趣的函数和曲线，这使得能够以直接的方式计算翘曲不变的弹性距离。我们区分了各种感兴趣的空间：原始空间，标准化后的环境空间，以及去掉一组变换后的商空间。使用环境空间中的高斯过程模型和翘曲函数的Dirichlet先验，我们探索了曲线和函数的贝叶斯推断。引入马尔可夫链蒙特卡罗算法，从后验模拟。我们还比较了平均形状的环境空间估计器和商空间估计器，并使用拉普拉斯近似解释了它们在许多实际问题中的常见相似性。进行了模拟研究，并在进化生物学中对小鼠脊椎轮廓的生长速率函数和形状分类进行了实用的比对。我们还比较了我们的贝叶斯方法和一些替代方法的性能。
Bayesian analysis of functions and curves is considered, where warping and other geometrical transformations are often required for meaningful comparisons. The functions and curves of interest are represented using the recently introduced square root velocity function, which enables a warping invariant elastic distance to be calculated in a straightforward manner. We distinguish between various spaces of interest: the original space, the ambient space after standardizing, and the quotient space after removing a group of transformations. Using Gaussian process models in the ambient space and Dirichlet priors for the warping functions, we explore Bayesian inference for curves and functions. Markov chain Monte Carlo algorithms are introduced for simulating from the posterior. We also compare ambient and quotient space estimators for mean shape, and explain their frequent similarity in many practical problems using a Laplace approximation. Simulation studies are carried out, as well as practical alignment of growth rate functions and shape classification of mouse vertebra outlines in evolutionary biology. We also compare the performance of our Bayesian method with some alternative approaches.