Probabilistic inference in high-dimensional state-space models is computationally challenging. For many spatiotemporal systems, however, prior knowledge about the dependency structure of state variables is available. We leverage this structure to develop a computationally efficient approach to state estimation and learning in graph-structured state-space models with (partially) unknown dynamics and limited historical data. Building on recent methods that combine ideas from deep learning with principled inference in Gaussian Markov random fields (GMRF), we reformulate graph-structured state-space models as Deep GMRFs defined by simple spatial and temporal graph layers. This results in a flexible spatiotemporal prior that can be learned efficiently from a single time sequence via variational inference. Under linear Gaussian assumptions, we retain a closed-form posterior, which can be sampled efficiently using the conjugate gradient method, scaling favourably compared to classical Kalman filter based approaches.

Abstract Movement ecologists study animals' movement to help understand their behaviours and interactions with each other and the environment. Data from GPS loggers are increasingly important for this. These data need to be processed, segmented and summarised for further visual and statistical analysis, often using predefined parameters. Usually, this process is separate from the subsequent visual and statistical analysis, making it difficult for these results to inform the data processing and to help set appropriate scale and thresholds parameters. This paper explores the use of highly interactive visual analytics techniques to close the gap between processing raw data and exploratory visual analysis. Working closely with animal movement ecologists, we produced requirements to enable data characteristics to be determined, initial research questions to be investigated, and the suitability of data for further analysis to be assessed. We design visual encodings and interactions to meet these requirements and provide software that implements them. We demonstrate these techniques with indicative research questions for a number of bird species, provide software, and discuss wider implications for animal movement ecology.

Understanding the limitations of environmental data is important for managing environmental systems effectively and for encouraging the responsible use of uncertain data. Explicit assessment of the uncertainties associated with environmental data, and their storage in a database, are therefore important. This paper presents a statistical framework for representing and simulating uncertain environmental variables. In general terms, an uncertain variable is completely specified by its probability distribution function (pdf). Pdfs are developed for objects with uncertain locations (‘positional uncertainty’) and uncertain attribute values (‘attribute uncertainty’). Objects comprising multiple space–time locations are separated into ‘rigid objects’, where positional uncertainty cannot alter the internal geometry of the object, and ‘deformable’ objects, where positional uncertainty can vary between locations in one object. Statistical dependence is allowed between uncertainties in multiple locations in one object. The uncertainties associated with attribute values are also modelled with pdfs. The type and complexity of these pdfs depend upon the measurement scale and the space–time variability of the uncertain attribute. The framework is illustrated with examples. A prototype software tool for assessing uncertainties in environmental data, storing them within a database, and for generating realizations for use in Monte Carlo studies is also presented.