Advanced random field models and practical Bayesian estimation

先进的随机场模型和实用的贝叶斯估计

• 批准号: 2617239
• 金额: --
• 依托单位: University of Edinburgh
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2617239
• 关键词: Advanced; random; field; models; practical

Bayesian methods involving Gaussian processes and random fields are commonly used when modelling spatial and spatiotemporal phenomena in a wide range of problems in ecology, geoscience, medical imaging, and epidemiology. However, realistic models can require non-stationary, non-Gaussian and non-linear behaviour that current methods are not equippedto handle efficiently. In this project, current models and methods based on Gaussian stochastic partial differential equations, numerical optimisation and integration, and currently implemented in the R-INLA software (http://r-inla.org and http://inlabru.org) will be extended to non-stationary and non-Gaussian models. An important aspect of computationallyefficient methods is to assess how close the numerical results are to the theoretically exact values, as well as to assess how well the estimated models mimic the real observed phenomena. This aspect will involve developing practical diagnostic measures for the approximations, and for assessing probabilistic spatial and temporal predictions.

涉及高斯过程和随机场的贝叶斯方法通常用于对生态、地球科学、医学成像和流行病学等领域的空间和时空现象进行建模。然而，现实模型可能需要非平稳、非高斯和非线性行为，而当前的方法无法有效地处理这些行为。在本项目中，目前在R-INLA软件（http://r-inla.org和http://inlabru.org）中实现的基于高斯随机偏微分方程、数值优化和积分的现有模型和方法将扩展到非平稳和非高斯模型。计算效率方法的一个重要方面是评估数值结果与理论精确值的接近程度，以及评估估计模型对实际观测现象的模拟程度。这方面将涉及为近似值开发实用的诊断措施，以及评估概率空间和时间预测。