Abstract

Scientists use imaging to identify objects of interest and infer properties of these objects. The locations of these objects are often measured with error, which when ignored leads to biased parameter estimates and inflated variance. Current measurement error methods require an estimate or knowledge of the measurement error variance to correct these estimates, which may not be available. Instead, we create a spatial Bayesian hierarchical model that treats the locations as parameters, using the image itself to incorporate positional uncertainty. We lower the computational burden by approximating the likelihood using a noncontiguous block design around the object locations. We use this model to quantify the relationship between the intensity and displacement of hundreds of atom columns in crystal structures directly imaged via scanning transmission electron microscopy (STEM). Atomic displacements are related to important phenomena such as piezoelectricity, a property useful for engineering applications like ultrasound. Quantifying the sign and magnitude of this relationship will help materials scientists more precisely design materials with improved piezoelectricity. A simulation study confirms our method corrects bias in the estimate of the parameter of interest and drastically improves coverage in high noise scenarios compared to non-measurement error models.

摘要

科学家使用成像来识别感兴趣的物体并推断这些物体的属性。这些对象的位置通常是有误差的，当被忽略时，会导致有偏差的参数估计和膨胀的方差。当前的测量误差方法需要对测量误差方差的估计或知识来纠正这些估计，而这可能是不可用的。相反，我们创建了一个空间贝叶斯层次模型，将位置视为参数，使用图像本身来包含位置不确定性。我们通过使用围绕对象位置的非连续块设计来近似似然性来降低计算负担。我们使用该模型来量化通过扫描透射电子显微镜 (STEM) 直接成像的晶体结构中数百个原子柱的强度和位移之间的关系。原子位移与压电等重要现象有关，压电性是一种对工程应用（如超声波）有用的特性。量化这种关系的符号和大小将有助于材料科学家更精确地设计具有改进压电性的材料。模拟研究证实，与非测量误差模型相比，我们的方法纠正了对感兴趣参数估计的偏差，并显着提高了高噪声场景中的覆盖率。对超声波等工程应用有用的属性。量化这种关系的符号和大小将有助于材料科学家更精确地设计具有改进压电性的材料。模拟研究证实，与非测量误差模型相比，我们的方法纠正了对感兴趣参数估计的偏差，并显着提高了高噪声场景中的覆盖率。对超声波等工程应用有用的属性。量化这种关系的符号和大小将有助于材料科学家更精确地设计具有改进压电性的材料。模拟研究证实，与非测量误差模型相比，我们的方法纠正了对感兴趣参数估计的偏差，并显着提高了高噪声场景中的覆盖率。