用随机流构建符合形状结构的演化模型，支持从观测数据推断演化参数。
Stochastics of shapes and Kunita flows
- 基于库尼塔流构造满足形状结构的随机演化过程
- 通过桥采样实现对观测数据的条件化，支持参数推断
- 适用于演化生物学中形态变化的统计建模与分析
随机形状演化过程在演化生物学等应用中具有重要意义，其中形态随进化过程呈随机变化。由于形状空间具有非线性和高维甚至无穷维特性，构造合适的随机形状过程在数学上极具挑战。本文定义并形式化了理想随机形状过程应满足的性质，并将其与库尼塔流联系起来：当库尼塔流作用于形状空间时，可自然生成满足这些性质的随机过程。同时，本文综述了其他相关形状随机过程，并展示了如何利用桥采样技术将形状随机过程条件化于观测数据，从而实现对随机动力学参数的统计推断。
原文摘要 · Abstract (English)
Stochastic processes of evolving shapes are used in applications including evolutionary biology, where morphology changes stochastically as a function of evolutionary processes. Due to the non-linear and often infinite-dimensional nature of shape spaces, the mathematical construction of suitable stochastic shape processes is far from immediate. We define and formalize properties that stochastic shape processes should ideally satisfy to be compatible with the shape structure, and we link this to Kunita flows that, when acting on shape spaces, induce stochastic processes that satisfy these criteria by their construction. We couple this with a survey of other relevant shape stochastic processes and show how bridge sampling techniques can be used to condition shape stochastic processes on observed data thereby allowing for statistical inference of parameters of the stochastic dynamics.
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