A generalized residual technique for analyzing complex movement models using earth mover's distance

摘要

1. Complex systems of moving and interacting objects are ubiquitous in thenatural and social sciences. Predicting their behavior often requires modelsthat mimic these systems with sufficient accuracy, while accounting for theirinherent stochasticity. Though tools exist to determine which of a set ofcandidate models is best relative to the others, there is currently no genericgoodness-of-fit framework for testing how close the best model is to the realcomplex stochastic system. 2. We propose such a framework, using a novel application of the Earthmover's distance, also known as the Wasserstein metric. It is applicable to anystochastic process where the probability of the model's state at time $t$ is afunction of the state at previous times. It generalizes the concept of aresidual, often used to analyze 1D summary statistics, to situations where thecomplexity of the underlying model's probability distribution makes standardresidual analysis too imprecise for practical use. 3. We give a scheme for testing the hypothesis that a model is an accuratedescription of a data set. We demonstrate the tractability and usefulness ofour approach by application to animal movement models in complex, heterogeneousenvironments. We detail methods for visualizing results and extracting avariety of information on a given model's quality, such as whether there is anyinherent bias in the model, or in which situations it is most accurate. Wedemonstrate our techniques by application to data on multi-species flocks ofinsectivore birds in the Amazon rainforest. 4. This work provides a usable toolkit to assess the quality of genericmovement models of complex systems, in an absolute rather than a relativesense.