Function Estimation and Inference in Helioseismology

太阳的声波振动包含了太阳内部声速、物质密度和角速度分布的信息。目前利用日震特征频率对太阳内部的这些特性进行成像的方法产生的图像可能与太阳相似，但这种技术的形式不确定性并不能准确地量化模型与事实之间可能存在的差异。这些方法也不能包含可能减少不确定性的物理限制。数据误差、建模算法的选择和理论近似对图像可靠性的影响在很大程度上未被探索；已公布的不确定性近似估计方法的可变性，其条件是太阳性质的特定参数表示和许多其他假设，而不考虑可能的偏差。斯塔克博士将开发和应用方法，在较少限制的假设下，研究太阳内部声速分布和太阳内部角速度分布的可变性和偏差。这种偏倚可以利用先前关于太阳的物理信息来控制，例如能量的界限或观测到的旋转引起的扁率。这项工作还将导致在存在无限维扰参数的情况下检验假设的新方法。

Stark, Philip 95-04410 Acoustic vibrations of the Sun contain information about the distributions of soundspeed, material density, and angular velocity within the Sun. Current methods for imaging these properties of the solar interior from helioseismic eigenfrequencies produce images that might resemble the Sun, but the formal uncertainties of the techniques do not accurately quantify possible differences between the models and the truth. Nor can the methods incorporate physical constraints that might reduce the uncertainty. The effects of data errors, choice of modeling algorithm, and theoretical approximations on the reliability of the images are largely unexplored; published uncertainties approximate the variability of the estimation method conditional on a particular parametric representation of the solar property and a host of other assumptions, without regard for possible biases. Dr. Stark will develop and apply methods to study both the variability and the bias of estimates of the distribution of soundspeed in the solar interior and the distribution of angular velocity in the solar interior, under less restrictive assumptions. The bias can be controlled using prior physical information about the Sun, such as bounds on either energy or observed rotationally-induced oblateness. The work will also lead to new methods to test hypotheses in the presence of infinite-dimensional nuisance parameters.