Probabilistic Modeling and Computational Methods in Environmental Statistics

这个项目考虑了统计学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)陈述的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。图像的概率建模是基于特征的统计结构，以便对图像进行压缩、重建/合成和统计分析。这些模型是从变换后的图像的基坐标之间的统计相关性导出的。具体地说，提出的任务是开发计算高效的独立分量分析，试图将图像转换为由高斯过程建模的一组独立分量。如果独立坐标系遵循ICA分解，则基本坐标之间的统计相关性将通过马尔可夫过程建模。作为研究的一部分，构建了验证度量来评估基于概率模型的图像合成和重建。这些度量是由Kullback-Leibler信息统计量的Edgeworth展开式和微分熵发展而来的。对声明的偏好评级数据的研究考虑了用于推断名义评级数据背后的经审查排名的概率结构的概率模型。开发的分层贝叶斯模型将需要计算高效的马尔可夫链蒙特卡罗例程，结合吉布斯抽样和Metropolis-Hastings步骤来拟合模型并得出适当的推断。该项目旨在开发计算高效的统计工具，用于地球物理图像和声明的偏好评级数据的概率建模。图像分析方法是由两个具体的地球物理问题驱动的，所开发的方法将被应用于：1)气象预报验证和2)地质分类。预报核实的目标是开发自动的、计算效率高的例行程序，以比较不同地理尺度的气象预报和观测，以评价气候预报模型。地质分类的目标是开发基于计算机学习和从训练数据集中提取特征的自动化、计算效率高的例程来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。处理既定偏好评级数据的方法是由项目评估中的两个问题驱动的，所开发的方法将应用于此：1)缓解全球气候变化影响的评级项目和2)华盛顿州改善鱼类种群的评级项目。在每个应用中，目标是通过考虑许多基本属性来评估环境项目，例如成本、物种影响和环境影响，仅举几例。统计分析将纳入该项目开发的概率和计量经济学模型和推理工具，以研究从两项研究的参与者那里获得的节目评级和偏好。该项目由数学科学部的统计计划和MPS的多学科活动办公室(OMA)共同支持。

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.