Function Estimation and Inference in Helioseismology

菲利普？斯塔克 95-04410太阳的声波振动包含了关于太阳内部声速、物质密度和角速度分布的信息。 目前从日震本征频率成像太阳内部这些特性的方法产生的图像可能类似于太阳，但技术的形式不确定性不能准确量化模型和真相之间可能存在的差异。 这些方法也不能纳入可能减少不确定性的物理约束。 数据误差的影响，建模算法的选择，和理论近似的可靠性的图像在很大程度上是未开发的;公布的不确定性近似的变化的估计方法的条件下，一个特定的参数表示的太阳属性和主机的其他假设，而不考虑可能的偏见。 斯塔克博士将开发和应用方法来研究太阳内部声速分布和太阳内部角速度分布估计的可变性和偏差，在限制较少的假设下。 这种偏差可以利用太阳先前的物理信息来控制，例如能量的界限或观测到的旋转引起的扁率。 这项工作还将导致新的方法来测试假设存在的无穷维滋扰参数。

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.