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

马尔可夫链蒙特卡罗方法将应用于统计推断问题，特别强调空间统计和贝叶斯计算。该项目与目标领域高度交叉，目标领域包括图像分析，无论是医学成像、遥感还是表面重建和测绘、农业试验数据分析和地理流行病学。对于贝叶斯后验分布中的多模态和稳健性等困难问题，存在着普遍的数学和计算方面的影响。马尔可夫链蒙特卡罗方法在统计物理学和随后的空间统计学中有着悠久的历史。现在，这些方法正以惊人的成功应用于一系列主流统计问题，除此之外，这些问题在数字上仍然难以解决。由于空间数据和测绘问题的性质，该项目具有高度的跨学科性质，重点是解决带有空间内涵的数据分析中的一些最困难的问题。

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.