81 research outputs found
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
Ensemble Kalman methods for high-dimensional hierarchical dynamic space-time models
We propose a new class of filtering and smoothing methods for inference in
high-dimensional, nonlinear, non-Gaussian, spatio-temporal state-space models.
The main idea is to combine the ensemble Kalman filter and smoother, developed
in the geophysics literature, with state-space algorithms from the statistics
literature. Our algorithms address a variety of estimation scenarios, including
on-line and off-line state and parameter estimation. We take a Bayesian
perspective, for which the goal is to generate samples from the joint posterior
distribution of states and parameters. The key benefit of our approach is the
use of ensemble Kalman methods for dimension reduction, which allows inference
for high-dimensional state vectors. We compare our methods to existing ones,
including ensemble Kalman filters, particle filters, and particle MCMC. Using a
real data example of cloud motion and data simulated under a number of
nonlinear and non-Gaussian scenarios, we show that our approaches outperform
these existing methods
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