Statistical inference and uncertainty quantification for complex process-based models using multiple data sets

通过使用能够代表土地使用的多种相互竞争的需求的复杂模型，可以促进对景观做出负责任的决定。关于土地使用的决定要求确定相互竞争的需求之间的权衡，并对其随时间的后果进行表征。在地图上通过时间表示结果的方法通常采用复杂模型的形式，例如随机计算机模拟。这种模型越来越多地被用来对现实世界的过程做出现实的预测，从涉及土地利用的社会生态系统到气候变化的影响。由于这些模型试图模拟真实物理系统的所有相关方面，因此它们可能涉及许多参数，其中一些参数很难正确设置。由于这些模型的最终目标是评估管理决策的可能后果，如风力涡轮机的布置，因此了解参数校准带来的不确定性至关重要。近似贝叶斯计算(ABC)是一种很有前途的技术，可以估计参数值及其可信区间，从而可以计算参数校准带来的不确定性。这一建议的总体目标是改进ABC或相关方法，使其足够快速和准确，使其可广泛用于复杂随机计算机模型的评估和校准，并量化其预测的不确定性。由于土地利用决策涉及到多个过程和多个数据集的考虑，这一过程变得复杂：本提案旨在开发专门针对这种情况设计的方法。该项目的最终目标是能够对实际、具有挑战性的应用程序的复杂模型的准确性进行拟合和评估，并使这种方法在实践中得到更广泛的应用。我们将与景观决策方案的研究人员以及其他参与景观决策建模的人员合作，将我们开发的方法应用到他们的模型中。我们的建议开发并运用了尖端的数学和统计方法，以校准复杂的模型，并量化其预测中因参数校准而产生的不确定性。

Making responsible decisions about landscapes is facilitated by the use of complex models able to represent multiple competing demands on land use. Decisions about land use require that trade-offs between competing demands be identified, and their consequences through time be characterised. Methods for representing consequences through time on maps generally take the form of complex models such as stochastic computer simulations. Such models are increasingly used to make realistic predictions about real world processes from socio-ecological systems involving land use to the effects of climate change. Because these models attempt to simulate all relevant aspects of a real physical system, they may involve many parameters, some of which will be difficult to set correctly. As the final objective of these models is to assess the possible consequences of management decisions, such as the placement of wind turbines, it is crucially important that the uncertainty introduced by calibrating parameters be understood.Approximate Bayesian Computation, or ABC, is a promising technique for estimating parameter values together with their credible intervals, and this allows calculation of the uncertainty deriving from parameter calibration. The overarching aim of this proposal is to improve ABC, or related approaches, to make them sufficiently fast and accurate that they can be widely used for the evaluation and calibration of complex stochastic computer models, and to quantify the uncertainty attached to their predictions. This process is complicated by the fact that making decisions about land use involves taking into account multiple processes and multiple datasets: this proposal aims to develop methods specifically designed for this situation.The end goal of the project is to be able to fit and evaluate the accuracy of complex models for real, challenging applications, and for this approach to be more widely used in practice. We will work with investigators in the landscape decision-making programme, and others involved in landscape decision modelling, to apply the methods we develop to their models. Our proposal develops and brings to bear cutting-edge mathematical and statistical methodologies to calibrate complex models, and to quantify the uncertainty in their predictions that derives from parameter calibration.