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Improved inference for nonparametric approaches to ecological dynamics.

Banff International Research Station for Mathematical Innovation and Discovery

Ecosystem-based approaches to management are desirable for many reasons. However quantitative approaches to ecosystem management are hampered by incomplete knowledge of the system state and uncertainty in the underlying dynamics. In principal, we can circumvent these difficulties using nonparametric approaches to model the uncertain dynamics and using time-delay embedding to implicit account for missing state variables. However, these methods are incredibly data-hungry and tend to be sensitive to observation noise. Here I propose to mitigate these practical obstacles a) by adopting a state-space perspective that allows us to partition observation and process uncertainty and b) by combining data from multiple locations using hierarchical and spatial modeling approaches. We find that noise reduction substantially improves attractor reconstruction and reduces bias in the estimation of Lyapunov exponents from noisy time series. Spatial-delay embedding significantly increases the time horizon over which useful predictions can be made compared to more traditional local embedding.

Mathematics; Partial differential equations; Biology and other natural sciences; Mathematical biology

video/mp4

Author affiliation: UC Santa Cruz

2020-09-09

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/75927

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/