Probabilistic Modeling and Computational Methods in Environmental Statistics

9978321该项目考虑统计方法在两个科学领域的发展和应用：1）地球物理数据的图像分析和2）所述偏好评级数据的建模。 反复出现的主题是研究每个数据结构背后的概率模型。 图像的概率建模基于特征的统计结构，以便压缩、重建/合成和统计分析图像。 该模型是从变换后的图像的基础坐标之间的统计依赖关系。 特别是，所提出的任务是开发一个计算效率高的独立分量分析，试图将图像转换成一组独立的高斯过程建模的组件。 如果相关坐标系遵循伊卡分解，则基础坐标之间的统计依赖性将通过马尔可夫过程建模。 作为研究的一部分，验证措施被构造为基于概率模型来评估图像合成和重建。 这些措施是从Kullback-Leibler信息统计量和微分熵的Edgeworth展开。 陈述偏好评级数据的研究考虑概率模型，用于推断名义评级数据下的删失排名的概率结构。 开发的分层贝叶斯模型将需要计算效率高的马尔可夫链蒙特卡罗程序，包括吉布斯抽样和Metropolis-Hastings步骤，用于拟合模型和绘制适当的推论。该项目旨在开发计算效率高的统计工具，用于地球物理图像和规定的偏好评级数据的概率建模。 图像分析方法的动机是两个具体的地球物理问题，开发的方法将被应用：1）气象预报验证和2）地质分类。 预测验证的目标是开发自动化的、计算效率高的程序，以比较不同地理尺度的气象预测和观测结果，从而评估气候预测模型。 地质分类的目标是开发自动化，计算效率高的例程，根据计算机学习和从训练数据集中提取特征对沉积物和岩层进行分类。 这两个应用程序中的每一个都将结合该项目在特征提取、压缩、重建/合成和统计建模方面开发的方法。 处理规定的偏好评级数据的方法是出于两个问题，在程序评估的方法将被应用：1）评级方案，以减轻全球气候变化的影响和2）评级方案，以改善鱼类种群在华盛顿州。 在每一个应用程序中，目标是通过考虑许多基本属性，如成本，物种影响和环境影响，仅举几例，对环境计划进行评估。 统计分析将结合该项目开发的概率和计量经济学模型和推理工具，以研究两项研究参与者的节目评级和偏好。 该项目由数学科学部统计计划和MPS多学科活动办公室（OMA）联合支持。

9978321This project considers the development and application of statistical methods in two scientific areas: 1) image analysis of geophysical data and 2) modeling of stated preference ratings data. The recurring theme is to study the probabilistic model underlying each data structure. The probabilistic modeling of images is based on the statistical structure of features in order to compress, reconstruct/synthesize, and statistically analyze the images. The models are derived from the statistical dependencies between the basis coordinates of transformed images. In particular, the proposed task is to develop a computationally efficient independent component analysis in an attempt to transform images into a set of independent components modeled by Gaussian processes. If the dependent coordinate systems follow an ICA decomposition, the statistical dependency between basis coordinates will be modeled through Markovian processes. As part of the study, validation measures are constructed to evaluate the image syntheses and reconstructions based on the probability models. These measures are developed from the Edgeworth expansion of the Kullback-Leibler information statistic and differential entropy. The study of stated preference ratings data considers probabilistic models for inferring the probabilistic structure of censored rankings underlying nominal ratings data. The hierarchical Bayesian models developed will require computationally efficient Markov chain Monte Carlo routines incorporating Gibbs sampling and Metropolis-Hastings steps for fitting the models and drawing appropriate inferences.The project aims at developing computationally efficient statistical tools for probabilistic modeling of geophysical images and stated preference ratings data. The image analysis methodologies are motivated by two specific geophysical problems to which the methods developed will be applied: 1) meteorological forecast verification and 2) geological classification. The goal for forecast verification is to develop automated, computationally efficient routines to compare meteorological forecasts and observations at different geographical scales towards an evaluation of climatological forecast models. The goal for geological classification is to develop automated, computationally efficient routines to classify sediments and rock formations based on computer learning and extraction of features from training data sets. Each of these twoApplications will incorporate methods developed by the project in feature extraction, compression, reconstruction/synthesis, and statistical modeling. Methodologies for handling stated preference ratings data are motivated by two problems in program valuation to which the methods developed will be applied: 1) rating programs for mitigating impacts of global climate change and 2) rating programs for improving fish populations in Washington State. In each application, the goal is the valuation of environmental programs through the consideration of many underlying attributes such as cost, species impact, and environmental impact, to name a few. The statistical analysis will incorporate the probabilistic and econometric models and inferential tools developed by the project to study program ratings and preferences elicited from participants in the two studies. This project is jointly supported by the Statistics Program in the Division of Mathematical Sciences and the Office of Multidisciplinary Activities (OMA) in MPS.