Spatial and Spatial-temporal Bayesian Point Process Models for Bioabudance and Other Applications

DMS 9626819沃尔伯特-贝叶斯分层模型被引入来考虑点过程模型的基本强度度量中的不确定性和空间变化。非齐次伽马过程随机场和更一般的具有无限可除分布的马尔可夫随机场被用来构造空间泊松点过程的正自相关强度度量，进而用于对单个事件的数量和位置进行建模。数据扩充方案和马尔可夫链蒙特卡罗数值方法被用来从贝叶斯后验分布和预测分布中产生样本。该方法在连续和离散两种情况下发展，并应用于森林生态等领域的问题。在许多调查领域，空间模式是统计数据的一个重要方面--疾病测绘，空间模式可以帮助我们了解特定疾病的易感原因或模式；农业，空间模式受土壤类型、经济和地区农业传统的影响，可以帮助我们预测产量；以及森林管理，空间模式帮助我们了解过去的土地利用，帮助我们预测问题(例如，对虫害的易感性)和管理机会(人口过多的物种的收获)。本研究利用计算硬件和算法以及数学概率理论方面的最新进展，开发用于探索空间模式数据的新的更好的统计模型和数值算法。新的统计模型和数值算法被应用于环境问题(研究联邦战略地区森林物种和生物多样性的变化模式)、疾病地图和交通理论(帮助预测不断发展的城市环境中的通勤交通流量，支持联邦民用基础设施战略地区)。

DMS 9626819 Wolpert Bayesian hierarchical models are introduced to account for uncertainty and spatial variation in the underlying intensity measure for point process models. Inhomogeneous gamma process random fields and, more generally, Markov random fields with infinitely-divisible distributions are used to construct positively autocorrelated intensity measures for spatial Poisson point processes, used in turn to model the number and location of individual events. A data augmentation scheme and Markov chain Monte Carlo numerical methods are employed to generate samples from Bayesian posterior and predictive distributions. The methods are developed in both continuous and discrete settings, and are applied to problems in forest ecology and other fields. Spatial patterns are an important aspect of statistical data in many fields of investigation-- disease mapping, where spatial patterns may help us learn about causes or patterns of susceptibility to specific diseases; agriculture, where spatial patterns, influenced by soil types, economics, and regional agricultural traditions, may help us predict yield; and forest management, where spatial patterns help us learn about past land-use and help us anticipate problems (for example, susceptibility to insect infestations) and management opportunities (the harvesting of overly populous species). The present research exploits recent advances in computing hardware and algorithms and in mathematical probability theory to develop new and better statistical models and numerical algorithms for exploring spatial pattern data. The new statistical models and numerical algorithms are applied to problems in the Environment (studying changing patterns of forest speciation and biodiversity in this Federal Strategic Area), Disease Mapping, and Transportation Theory (helping to predict commuter traffic flow in an evolving urban environment, supporting the Federal Strategic Area of Civil Infrastructure).