Generalized Nonlinear Models: Theory, Computation and Extensions

该项目将为一大类统计模型开发一种系统的方法，该方法统一并扩展了为广泛的科学学科的特定应用开发的许多方法。广义非线性模型的类别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。目前的项目将为这种模式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，包括图形方法，将扩展到这一更广泛的模型类别，以及系统处理模型中未明确预测的变异（所谓的随机效应）的方法。将特别注意与当前实际工作直接相关的实例，特别是包括乘法项的模型;这些模型最近在实验心理学、作物科学和社会学等不同的研究领域都很重要。贯穿所有工作的一个关键线索将是统计模型的过度参数化表示的新颖使用，旨在允许自然地构建富有想象力的建模策略，而无需在每个步骤中过度关注技术细节（通常与参数可识别性有关）。研究结果将出现在同行审查的科学文献和有充分文件记录的开放源码软件中，从而使这些方法的发展立即提供给从业人员。

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.