贝叶斯空间模型的共轭先验模型

English | 2024 | ISBN: 978-3-031-65418-3 | 237 pages | PDF EPUB (True) | 24 MB

This book offers a comprehensive overview of statistical methodology for modelling and evaluating spatial variables useful in a variety of applications. These spatial variables fall into three categories: continuous, like terrain elevation; events, like tree locations; and mosaics, like medical images.

Definitions and discussions of random field models are included for each of these three previously mentioned spatial variable types. Moreover, the readers will have access to algorithms suitable for applying this methodology in practical problem solving, and the computational efficiency of these algorithms are discussed.

The presentation is made in a consistent predictive Bayesian framework, which allows separate modelling of the observation acquisition procedure, as a likelihood model, and of the spatial variable characteristics, as a prior spatial model. The likelihood and prior models uniquely define the posterior spatial model, which provides the basis for spatial simulations, spatial predictions with associated precisions, and model parameter inference. The emphasis is on Bayesian spatial modelling with conjugate pairs of likelihood and prior models that are analytically tractable and hence suitable for data abundant spatial studies. Alternative methods frequently used in spatial statistics are presented using a unified notation.

The book is suitable as a textbook for a ‘Spatial Statistics’ course at the MSc or PhD level, as it also includes algorithm descriptions, project texts, and exercises.

这本书提供了全面的统计方法概览，用于建模和评估在各种应用中使用的空间变量。这些空间变量分为三类：连续型的，比如地形高度；事件型的，比如树木的位置；以及镶嵌型的，比如医学图像。 书中包括了对这三种之前提到的空间变量类型的随机场模型的定义与讨论。此外，读者还将获得适用于实际问题解决的算法，并讨论这些算法的计算效率。 呈现方式采用一致的概率预测框架，在此框架下可以分别建模观察获取过程（作为似然模型）和空间变量特性（作为先验空间模型）。似然模型和先验模型共同定义了后验空间模型，这为空间模拟、带有精度的空间预测以及模型参数推断提供了基础。重点在于使用易于计算分析且适用于数据丰富性空间研究的似然与先验模型配对的贝叶斯空间建模方法。另外还展示了常用的空间统计学方法，并采用统一的记号。 这本书适合作为“空间统计”课程的教科书，因为它还包括了算法描述、项目文本和练习内容。

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