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Spatio-temporal data indexed by sampling locations and sampling time points are encountered in many scientific disciplines such as climatology, environ- mental sciences, and public health. Here, we propose a novel spatio-temporal expanding distance (STED) asymptotic framework for studying the proper- ties of statistical inference for nonstationary spatio-temporal models. In particular, to model spatio-temporal dependence, we develop a new class of locally stationary spatio-temporal covariance functions. The STED asymp- totic framework has a fixed spatio-temporal domain for spatio-temporal pro- cesses that are globally nonstationary in a rescaled fixed domain and locally stationary in a distance expanding domain. The utility of STED is illus- trated by establishing the asymptotic properties of the maximum likelihood estimation for a general class of spatio-temporal covariance functions. A simulation study suggests sound finite-sample properties and the method is applied to a sea-surface temperature dataset.
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Estimating spatio-temporal fields through reinforcement learning
Prediction and estimation of phenomena of interest in aquatic environments are challenging since they present complex spatio-temporal dynamics. Over the past few decades, advances in machine learning and data processing contributed to ocean exploration and sampling using autonomous robots. In this work, we formulate a reinforcement learning framework to estimate spatio-temporal fields modeled by partial differential equations. The proposed framework addresses problems of the classic methods regarding the sampling process to determine the path to be used by the agent to collect samples. Simulation results demonstrate the applicability of our approach and show that the error at the end of the learning process is close to the expected error given by the fitting process due to added noise.
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- PAR ID:
- 10358100
- Date Published:
- Journal Name:
- Frontiers in Robotics and AI
- Volume:
- 9
- ISSN:
- 2296-9144
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3389/frobt.2022.878246
