建模时空数据：马尔可夫随机场、客观贝叶斯方法和多尺度模型

English | 2024 | ISBN: 9781032623443 | 293 pages | True PDF | 20.3 MB

Several important topics in spatial and spatio-temporal statistics developed in the last 15 years have not received enough attention in textbooks. Modeling Spatio-Temporal Data: Markov Random Fields, Objectives Bayes, and Multiscale Models aims to fill this gap by providing an overview of a variety of recently proposed approaches for the analysis of spatial and spatio-temporal datasets, including proper Gaussian Markov random fields, dynamic multiscale spatio-temporal models, and objective priors for spatial and spatio-temporal models. The goal is to make these approaches more accessible to practitioners, and to stimulate additional research in these important areas of spatial and spatio-temporal statistics.

Key topics

Proper Gaussian Markov random fields and their uses as building blocks for spatio-temporal models and multiscale models. Hierarchical models with intrinsic conditional autoregressive priors for spatial random effects, including reference priors, results on fast computations, and objective Bayes model selection. Objective priors for state-space models and a new approximate reference prior for a spatio-temporal model with dynamic spatio-temporal random effects. Spatio-temporal models based on proper Gaussian Markov random fields for Poisson observations. Dynamic multiscale spatio-temporal thresholding for spatial clustering and data compression. Multiscale spatio-temporal assimilation of computer model output and monitoring station data. Dynamic multiscale heteroscedastic multivariate spatio-temporal models. The M-open multiple optima paradox and some of its practical implications for multiscale modeling. Ensembles of dynamic multiscale spatio-temporal models for smooth spatio-temporal processes. The audience for this book are practitioners, researchers, and graduate students in statistics, data science, machine learning, and related fields. Prerequisites for this book are master's-level courses on statistical inference, linear models, and Bayesian statistics. This book can be used as a textbook for a special topics course on spatial and spatio-temporal statistics, as well as supplementary material for graduate courses on spatial and spatio-temporal modeling.

近年来，在空间和时空统计学领域发展的一些重要话题，尚未在教科书中获得足够的关注。《建模时空数据：马尔可夫随机场、目标贝叶斯及多尺度模型》旨在填补这一空白，通过提供一系列最近提出的用于分析空间和时空数据集的方法的概述，包括合适的高斯马尔可夫随机场、动态多尺度时空模型以及空间和时空模型的目标先验。目的是使这些方法更加易于实践者理解，并在重要的空间和时空统计学领域促进更多研究。 关键话题 合适的高斯马尔可夫随机场及其作为时空模型和多尺度模型构建块的用途。 包括参考先验、快速计算结果和目标贝叶斯模型选择在内的具有内在条件自回归先验的层次模型，用于处理空间随机效应。 状态空间模型的目标先验以及一种新的近似参考先验，适用于包含动态时空随机效应的空间时序模型。 基于合适的高斯马尔可夫随机场的时空模型，用于分析泊松观测值的数据集。 针对空间聚类和数据压缩问题的时空多尺度阈值化方法。 将计算机模型输出与监测站数据进行时空融合以及监控。 适用于多元动态多尺度时空模型中的异方差性目标贝叶斯模型。 M-开放多个最佳点悖论及其在多尺度建模中的一些实际影响。 用于光滑时空过程的动态多尺度时空建模混合体。 本书的目标读者是统计学、数据科学、机器学习及相关领域中从事研究和教学的实践者、研究人员及研究生。本教材要求的基础课程包括统计推断、线性模型和贝叶斯统计学。这本书可以作为关于空间和时空统计学的专题课程教科书，也可以用作空间和时空建模硕士课程的补充材料。

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