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

DMS 9626819 Wolpert Bayesian分层模型被引入来解释点过程模型的基本强度测量中的不确定性和空间变化。 非齐次伽马过程随机场，更一般地说，马尔可夫随机场与无限可分的分布被用来构建正自相关强度措施的空间泊松点过程，反过来又用来模拟个别事件的数量和位置。 一个数据增强计划和马尔可夫链蒙特卡罗数值方法来生成样本的贝叶斯后验和预测分布。 这些方法是在连续和离散环境中开发的，并应用于森林生态学和其他领域的问题。 空间模式是许多调查领域统计数据的一个重要方面-疾病绘图，空间模式可帮助我们了解对特定疾病的易感性的原因或模式;农业，受土壤类型、经济和区域农业传统影响的空间模式可帮助我们预测产量;空间格局有助于我们了解过去的土地使用情况，并帮助我们预测问题（例如，易受虫害影响）和管理机会（过度繁殖物种的收获）。 本研究利用最新进展的计算硬件和算法，并在数学概率论开发新的和更好的统计模型和数值算法，探索空间模式数据。 新的统计模型和数值算法被应用于环境问题（研究森林物种形成和生物多样性的变化模式在这个联邦战略领域），疾病地图，和运输理论（帮助预测通勤交通流量在不断发展的城市环境，支持民用基础设施的联邦战略领域）。

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).