Collaborative Research: Shape-Based Imputation and Estimation of Fragmented, Noisy Curves with Application to the Reconstruction of Fossil Bovid Teeth

合作研究:基于形状的碎片、噪声曲线的插补和估计,应用于化石牛牙齿的重建

基本信息

  • 批准号:
    2015320
  • 负责人:
  • 金额:
    $ 7.33万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2020
  • 资助国家:
    美国
  • 起止时间:
    2020-09-01 至 2025-02-28
  • 项目状态:
    未结题

项目摘要

Statistical analysis of shape data is relevant to a wide array of fields including biology, anthropology, chemistry, and medicine, to name just a few. Current methods for analyzing shape data generally focus on shapes that are fully observed. This project will develop methods for analyzing shapes that are only partially observed. Traditional missing data techniques are not applicable in the shape setting when 1) shapes are defined by functions and 2) shape-preserving transformations (e.g. translation, rotation, scaling, re-parameterization, etc.) must be accounted for. This project will formalize and harness this perspective for data obtained from fragmentary fossil tooth images of the Family Bovidae (antelopes and buffaloes) as partially observed curves, representing the outlines of imaged objects, possibly with measurement error. The resulting taxonomic identifications will generate more robust estimates of the ecologically sensitive bovids. These improved estimates, in turn, afford novel insight into the paleoenvironmental context of early human evolution. The main goal of this project is to develop statistical methods for the analysis of partially observed shapes (i.e., fragmented curves). This goal will be accomplished via two different approaches: 1) developing computational methods for imputing a fragmented curve by matching and completing it based on a template or donor curve obtained from a sample of fully observed curves, and 2) developing Bayesian model-based methods for estimation and classification of the shape of a noisy, fragmented curve using an empirical prior on the overall shape of the curve. Both approaches will be built using Riemannian geometric tools for shape analysis that ensure proper invariance to shape preserving transformations including translation, scaling (when appropriate), rotation, and re-parameterization. These methods will be developed with the motivating application of the analysis and taxonomic classification of fractured and complete fossil teeth from the Family Bovidae. By generating a proxy for paleoenvironmental conditions, the project seeks to advance our understanding of the relationship between environmental change and hominin evolution.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
形状数据的统计分析涉及广泛的领域,包括生物学、人类学、化学和医学,仅举几例。当前用于分析形状数据的方法一般集中在完全观察到的形状上。该项目将开发用于分析仅部分观察到的形状的方法。当1)形状由函数定义并且2)形状保持变换(例如,平移、旋转、缩放、重新参数化等)时,传统的缺失数据技术不适用于形状设置。必须解释清楚。该项目将对从牛科动物(羚羊和水牛)的零碎化石牙齿图像中获得的数据进行正式处理和利用,将其作为部分观察曲线,表示成像物体的轮廓,可能存在测量误差。由此产生的分类学鉴定将对生态敏感的牛类产生更可靠的估计。这些改进的估计反过来又为早期人类进化的古环境背景提供了新的见解。该项目的主要目标是开发统计方法,用于分析部分观察到的形状(即断续的曲线)。这一目标将通过两种不同的方法来实现:1)开发计算方法,通过基于从完全观察到的曲线样本获得的模板或施主曲线来匹配和完善分段曲线,来输入分段曲线;以及2)开发基于贝叶斯模型的方法,使用曲线整体形状的经验先验来估计和分类噪声的、分段的曲线的形状。这两种方法都将使用黎曼几何工具进行形状分析,以确保形状保持变换的适当不变性,包括平移、缩放(适当时)、旋转和重新参数化。这些方法将随着对牛科断裂和完整化石牙齿的分析和分类的激励性应用而发展。通过生成古环境条件的替代物,该项目试图促进我们对环境变化和原始人进化之间关系的理解。该奖项反映了NSF的法定使命,并通过使用基金会的智力优势和更广泛的影响审查标准进行评估,被认为值得支持。

项目成果

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Ofer Harel其他文献

Guest Editorial: Articles selected from the 2020 International Conference on Health Policy Statistics
Now You See It, Now You Don’t: A Simulation and Illustration of the Importance of Treating Incomplete Data in Estimating Race Effects in Sentencing
现在您看到了,现在您没有:模拟和说明在估计量刑中的种族影响时处理不完整数据的重要性

Ofer Harel的其他文献

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{{ truncateString('Ofer Harel', 18)}}的其他基金

Collaborative Research: Statistical Analysis of Partially Observed Shapes in Two Dimensions
合作研究:二维部分观察形状的统计分析
  • 批准号:
    1811969
  • 财政年份:
    2018
  • 资助金额:
    $ 7.33万
  • 项目类别:
    Standard Grant

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