Generalized Nonlinear Models: Theory, Computation and Extensions

该项目将对一大类统计模型制定一种系统的方法，统一和扩展为各种科学学科的特定应用而开发的许多方法。广义非线性模型包括统计方法的一些基石，特别是广义线性模型和参数非线性回归，作为突出的子类。目前的项目将为这类模型中的近似推理和计算制定统一的方法。此外，总结和显示分析结果的创新方法，包括图解方法，将推广到这类更广泛的模型，以及对模型中没有明确预测的变化(所谓的随机效应)进行系统处理的方法。将特别注意与当前实际工作直接相关的实例，特别是包括乘法术语的模型；最近，这些实例在实验心理学、作物科学和社会学等各种研究领域都很重要。贯穿所有工作的一个关键主线将是对统计模型的过度参数表示的新颖使用，其目的是允许自然地构建富有想象力的建模战略，而不需要在每一步过分注意技术细节(通常与参数可辨识性有关)。研究结果将出现在同行评议的科学文献和完全有文件记录的开放源码软件中，从而使从业者可以立即获得这些方法的发展。

This project will develop a systematic approach to a large class of statistical models, which unifies and extends many methods that have been developed for particular applications across a wide range of scientific disciplines. The class of generalized nonlinear models includes as prominent sub-classes some of the cornerstones of statistical methodology, notably generalized linear models and parametric nonlinear regression. The current project will develop unified methods for approximate inference and for computation in such models. In addition, innovative methods for summary and display of the results of an analysis, including graphical methods, will be extended to this broader class of models, as will methods for the systematic treatment of variation that is not explicitly predicted within the model (so-called random effects ). Particular attention will be paid to instances that are of direct relevance to current practical work, notably models which include multiplicative terms; these have been important recently in research fields as diverse as experimental psychology, crop science and sociology, for example. A key thread running through all of the work will be the novel use of over-parameterized representations of statistical models, designed to allow imaginative modelling strategies to be constructed naturally and pursued without the need to pay undue attention to technical details (typically connected with parameter identifiability) at each step. The results of the research will appear in the peer-reviewed scientific literature and in fully documented open-source software, thus making these methodological developments immediately available to practitioners.