Asymptotic Theory of Penalized Splines and Calibration of Computationally Expensive Models

调查员研究两个领域。第一个是惩罚样条的大样本理论。二是计算昂贵模型的贝叶斯校正和不确定性分析。将单变量惩罚样条理论推广到二次、高次样条和高阶差分惩罚。将单变量理论推广到加性模型和双变量回归。针对测量误差异方差的反褶积问题，提出了惩罚样条法。在时空相关性、环境输入测量误差和多重响应的情况下，研究了贝叶斯校准和不确定度分析。样条是定义曲线和曲面的数学工具。例如，在计算机辅助设计中，使用样条来描述汽车车身的形状。在统计学中，样条用于描述变量之间的曲线关系。例如，最近一项关于儿童血铅浓度与智商之间关系的研究使用了样条曲线，并发现了一个意想不到的重要结果。剂量-反应曲线在低剂量时最陡峭，这意味着，在低剂量下，智商随铅浓度增加而下降的速度比以前认识到的要快。这一出乎意料的发现表明，如果环境中的铅浓度降低，那么儿童智力发展的改善程度将超出先前的想象。样条曲线在这类研究中特别有用，因为它们可以结合对母亲智商和其他因素的调整，以及对单个受试者的多个智商测量之间的相关性。研究者研究样条是为了提高估计的精度和扩大适用范围。复杂模型的校准用于各种应用，例如石油勘探和流域管理。PI和他的同事们研究了坎农斯维尔流域，这是纽约市的饮用水源。模型的校准意味着使用数据来估计未知参数。不确定性分析测量估计的精度。校正和不确定度分析是必要的，以便这些模型可以用于管理。例如，Cannonsville水库的模型帮助纽约市管理流域以保持水，从而不需要昂贵的过滤系统。

The investigator studies two areas. The first is the large-sample theory of penalized splines. The second is Bayesian calibration and uncertainty analysis for computational expensive models. The theory for univariate penalized splinesis generalized to quadratic and higher degree splines and to higher order difference penalties. The univariate theory is extended to additive models and to bivariate regression. Penalized splines methods are developed for deconvolution with heteroscedastic measurement error. Bayesian calibration anduncertainty analysis is studied in the cases of spatial-temporal correlations, measurement error in environmental inputs, and multiple responses.Splines are mathematical tools for defining curves and surfaces. Splines are used, for example, to describe the shape of an automobile body in computer-assisted design. In statistics, splines are used to describe curved relationships between variables. For example, a recent study of therelationship between blood-lead concentration and IQ in children used splines and found an unexpected and important result. The dose-response curve is steepest at low doses, meaning that, at low doses, IQ declines with increasing lead concentrations more rapidly than previously realized. This unanticipated finding implies that, if environmental lead concentrations are reduced, then the intellectual development of children will be improved by an amount exceeding what was previously thought. Splines are particularly useful in thistype of study because they can be combined with adjustments for maternal IQ and other factors and for correlations between multiple IQ measurements on a single subject. The investigator studies splines to improve the precision of estimation and to extend the range of applicability. Calibration of complexmodels is used in a variety of applications including, for example, petroleum exploration and management of watersheds. The PI and his colleagues study the Cannonsville watershed, a source of drinking water for New York City. Calibration of a model means using data to estimate unknown parameters. Uncertainty analysis measures the precision of the estimates. Calibration and uncertainty analysis is needed so that these models can be used for management. For example, the model for the Cannonsville Reservoir helps NYC manage the watershed to maintain water so that expensive filtration systems are not needed.