Mathematical Sciences: Robustness and Scale in Spatial Applications of Markov Chain Monte Carlo for Bayesian Inference

建议：DMS9505114 PI：Dave Higdon Institution：Duke University标题：马尔科夫链在空间应用中的稳健性和规模蒙特卡罗贝叶斯推理摘要：拟议的研究为空间系统的贝叶斯推理开发了灵活的先验分布。从建模的角度来看，简单马尔可夫随机场(MRF)上的混合空间先验是在两个不同的背景下发展起来的。在第一种情况下，当空间过程中存在异常和异质性时，将构建混合模型以允许稳健推理。在第二种情况下，将考虑不同尺度上的混合物，以便在进行推断时可以严格地将MRF的尺度作为一个参数。只有马尔可夫链蒙特卡罗(MCMC)的最新进展才使从这样的模型中进行推断成为可能。将考虑在农业、成像和环境监测方面的应用。拟议的研究将制定分析空间数据的统计方法，这些空间数据结合了不同尺度的信息。开发适用于农业的空间模型，成像(例如。遥感和医学成像)、环境监测和环境趋势评估是本研究的主要目标。目前的统计方法通常需要限制性假设，这往往使在这些领域进行正式分析变得困难或不可能。这种方法将放松这些假设。综合各种尺度的信息的一个主要动机是处理用于环境监测的地理信息系统。这样的系统总是包含不同尺度的数据，这些数据可以并入分析。

Proposal: DMS9505114 PI: Dave Higdon Institution: Duke University Title: Robustness and Scale in Spatial Applications of Markov Chain Monte Carlo for Bayesian Inference Abstract: The proposed research develops flexible prior distributions for Bayesian inference for spatial systems. From the modeling standpoint, spatial priors that are mixtures over simple Markov random fields (MRF's) are developed in two distinct contexts. In the first, mixtures will be constructed to allow robust inference when anomalies, and heterogeneity are present in the spatial process. In the second context, mixtures over different scales will be considered, so that the scale of the MRF can be rigorously treated as a parameter when making inference. Only very recent advances in Markov chain Monte Carlo (MCMC) make inference from such models possible. Applications in agriculture, imaging and environmental monitoring will be considered. The proposed research will develop statistical methodologies for analyzing spatial data which combines information at various scales. Development of spatial models suitable for agriculture, imaging (eg. remote sensing and medical imaging), environmental monitoring and assessing environmental trends are main goals of this research. Current statistical methods typically require restrictive assumptions which often make formal analyses in these areas difficult or impossible. This methodology will relax these assumptions. A primary motivation for combining information from various scales is for dealing with geographical information systems used for environmental monitoring. Such systems invariably contain data at varying scales which can be incorporated in the analysis.