Bayesian Recurrent Neural Network Models for Forecasting and Quantifying Uncertainty in Spatial-Temporal Data

Recurrent neural networks (RNNs) are nonlinear dynamical models commonly used in the machine learning and dynamical systems literature to represent complex dynamical or sequential relationships between variables. More recently, as deep learning models have become more common, RNNs have been used to forecast increasingly complicated systems. Dynamical spatio-temporal processes represent a class of complex systems that can potentially benefit from these types of models. Although the RNN literature is expansive and highly developed, uncertainty quantification is often ignored. Even when considered, the uncertainty is generally quantified without the use of a rigorous framework, such as a fully Bayesian setting. Here we attempt to quantify uncertainty in a more formal framework while maintaining the forecast accuracy that makes these models appealing, by presenting a Bayesian RNN model for nonlinear spatio-temporal forecasting. Additionally, we make simple modifications to the basic RNN to help accommodate the unique nature of nonlinear spatio-temporal data. The proposed model is applied to a Lorenz simulation and two real-world nonlinear spatio-temporal forecasting applications

Bayesian Learning and Predictability in a Stochastic Nonlinear Dynamical Model

Bayesian inference methods are applied within a Bayesian hierarchical modelling framework to the problems of joint state and parameter estimation, and of state forecasting. We explore and demonstrate the ideas in the context of a simple nonlinear marine biogeochemical model. A novel approach is proposed to the formulation of the stochastic process model, in which ecophysiological properties of plankton communities are represented by autoregressive stochastic processes. This approach captures the effects of changes in plankton communities over time, and it allows the incorporation of literature metadata on individual species into prior distributions for process model parameters. The approach is applied to a case study at Ocean Station Papa, using Particle Markov chain Monte Carlo computational techniques. The results suggest that, by drawing on objective prior information, it is possible to extract useful information about model state and a subset of parameters, and even to make useful long-term forecasts, based on sparse and noisy observations