Non-Stationary Models for Spatial Statistics and Bayesian Image Analysis

NSF DMS-9704425 空间统计与贝叶斯图像的非平稳模型 分析. 大卫希登杜克大学 翻译后摘要：本研究开发了各向异性的空间模型，完全贝叶斯推理与应用 在空间和时间上相互关联的数据。 两 采取不同的方向。 第一，继续 以前的研究，马尔可夫随机场先验格 被认为是建模过程中偶尔大 水平的变化。 第二，使用构造性卷积 方法，开发连续模型，允许 非平稳性和相关性结构， 空间（或时间）。 使用这种模型进行推理需要 一个解释了这些模型的灵活性或变化性的不确定性。 研究的一个关键部分是开发将这种不确定性来源纳入统计分析的方法。 对随空间和时间演变的现象进行统计建模，在医学成像、环境监测和检测全球气候随时间的变化等领域至关重要。 统计学中的大多数空间模型都假设，在给定区域内，空间（可能还有时间）模式的基本属性在该区域内保持不变。 虽然这在有限的区域内是一个有用的简化，但在更大的范围内，这样的假设往往会导致 在一个令人不满意的模式。 这项研究将建立统计模型，解释空间现象性质的突然变化。 此外，模型将 开发了允许空间过程的属性在空间位置上演变的方法。 该研究将为大尺度空间和时空的建模提供更真实的模型 现象。 将这些模型拟合到大型数据集需要 大量的计算工作量，并且可能依赖于高性能 计算资源。 全球海洋气候变化的应用， 农业、遗传学和医学成像将被考虑。

NSF DMS-9704425 Non-Stationary Models for Spatial Statistics and Bayesian Image Analysis. David Higdon Duke University Abstract: This research develops anisotropic spatial models for fully Bayesian inference with applications to data which are correlated over space and time. Two distinct directions are taken. First, in continuation of previous research, Markov random field priors for lattices are considered for modeling processes with occasional large shifts in level. Second, using a constructive convolution approach, continuous models are developed that allow non-stationarity and correlation structure that can vary over space (and/or time). Using such models for inference requires that one account for uncertainty about just how flexible or varying such models are. A key part of the research is developing methods which incorporate this source of uncertainty in the statistical analysis. Statistical modeling of phenomena that evolve over space and possibly time is critical in areas such as medical imaging, environmental monitoring, and detecting changes over time in global climate. Most spatial models in statistics assume that over a given area, the underlying properties of a spatial (and possibly temporal as well) pattern remain unchanged over the region. Though this is a useful simplification over limited regions, on a larger scale such an assumption often results in an unsatisfactory model. This research will develop statistical models that account for abrupt changes in the nature of the spatial phenomenon. Also, models will be developed that allow properties of the spatial process to evolve over spatial location. This research will lead to more realistic models for large scale spatial and spatio-temporal phenomena. Fitting these models to large datasets will require a substantial computing effort and will likely rely high performance computing resources. Applications in global ocean climate change, agriculture, genetics, and medical imaging will be considered.