Function Estimation and Inference in Helioseismology

斯塔克，菲利普95-04410太阳的声学振动包含有关太阳内部声速、物质密度和角速度分布的信息。目前根据日震特征频率成像太阳内部这些特性的方法产生的图像可能与太阳相似，但这些技术在形式上的不确定性并不能准确量化模型和真相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约束。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还没有被探索；已公布的不确定因素近似于估计方法的可变性，条件是太阳属性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各种方法，在限制性较低的假设下，研究太阳内部声速分布和角速度分布估计值的可变性和偏差。可以使用关于太阳的先前物理信息来控制偏差，例如能量界限或观测到的旋转诱导扁率。这项工作还将导致在存在无限维扰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.