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Open AccessFeature PaperArticle

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

1
Jupiter Intelligence, Boulder, CO 80302, USA
2
Department of Statistics, University of Missouri, Columbia, MO 65211, USA
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(2), 184; https://doi.org/10.3390/e21020184
Received: 29 December 2018 / Revised: 3 February 2019 / Accepted: 12 February 2019 / Published: 15 February 2019
(This article belongs to the Special Issue Spatial Information Theory)
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. 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. View Full-Text
Keywords: recurrent neural network; Bayesian machine learning; nonlinear dynamical models; long-lead forecasting; spatial-temporal recurrent neural network; Bayesian machine learning; nonlinear dynamical models; long-lead forecasting; spatial-temporal
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McDermott, P.L.; Wikle, C.K. Bayesian Recurrent Neural Network Models for Forecasting and Quantifying Uncertainty in Spatial-Temporal Data. Entropy 2019, 21, 184.

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