Mathematical Sciences: Image Analysis, Spatial Statistics, and Bayesian Inference

马尔可夫链蒙特卡罗方法将应用于问题 在特别强调空间统计推断中， 统计和贝叶斯计算。 该项目高度 跨学科的目标领域，包括图像分析， 无论是从医学成像、遥感还是地表 重建和映射，数据分析， 农业实验和地理流行病学。 有一般的数学和计算的影响， 困难的问题，如多模态和鲁棒性， 贝叶斯后验分布 马尔可夫链蒙特卡罗方法有着悠久的历史， 统计物理学和空间统计学。 现在 这些技术在大范围的应用中取得了惊人的成功 主流的统计问题， 否则就很难处理 这个项目，这是高度 由于空间数据的性质， 地图问题，重点是解决一些最困难的 在分析数据的问题，携带空间 内涵

Markov chain Monte Carlo methods will be applied to problems in statistical inference with particular emphasis on spatial statistics and Bayesian computation. This project is highly interdisciplinary with target areas that include image analysis, whether from medical imaging, remote sensing or surface reconstruction and mapping, the analysis of data from agricultural experiments and from geographical epidemiology. There are general mathematical and computational implications for difficult issues such as multi-modality and robustness in Bayesian posterior distributions. Markov chain Monte Carlo methods have a long history in statistical physics and subsequently in spatial statistics. Now these are being applied with spectacular success to a vast range of mainstream statistical problems that have remained numerically intractable otherwise. This project, which is highly interdisciplinary because of the nature of spatial data and mapping problems, focuses on the solutions to some of the hardest problems in the analysis of data which carry spatial connotations.