arXiv subjects

Jeffrey Covington

Publications and source records attributed to Jeffrey Covington.

4 recordsLinked to original sources

arXiv2025

Estimating dynamic transmission rates with a Black-Karasinski process in stochastic SIHR models using particle MCMC

Compartmental models are effective in modeling the spread of infectious pathogens, but have remaining weaknesses in fitting to real datasets exhibiting stochastic effects. We propose a stochastic SIHR model with a dynamic transmission rate, where the rate is modeled by the Black-Karasinski (BK) process - a mean-reverting stochastic process with a stable equilibrium distribution, making it well-suited for modeling long-term epidemic dynamics. To generate sample paths of the BK process and estimate static parameters of the system, we employ particle Markov Chain Monte Carlo (pMCMC) methods due to their effectiveness in handling complex state-space models and jointly estimating parameters. We designed experiments on synthetic data to assess estimation accuracy and its impact on inferred transmission rates; all BK-process parameters were estimated accurately except the mean-reverting rate. We also assess the sensitivity of pMCMC to misspecification of the mean-reversion rate. Our results show that estimation accuracy remains stable across different mean-reversion rates, though smaller values increase error variance and complicate inference results. Finally, we apply our model to Arizona flu hospitalization data, finding that parameter estimates are consistent with published survey data.

stat.ME↗

arXiv2024

Probabilistic Eddy Identification with Uncertainty Quantification

Mesoscale eddies are critical in ocean circulation and the global climate system. Standard eddy identification methods are usually based on deterministic optimal point estimates of the ocean flow field. However, uncertainty exists in estimating the flow field due to noisy, sparse, and indirect observations and turbulent flow models. Because of the intrinsic strong nonlinearity in the eddy identification diagnostics, even a small uncertainty in estimating the flow field can cause a significant error in the identified eddies. This paper presents a general probabilistic eddy identification framework that adapts existing identification methods to incorporate uncertainty into the diagnostic, emphasizing the interaction between the uncertainty in state estimation and the nonlinearity in diagnostics for affecting the identification results. The probabilistic eddy identification framework starts by sampling an ensemble of flow realizations from the probabilistic state estimation, followed by applying traditional nonlinear eddy diagnostics to individual realizations. The corresponding eddy statistics are then aggregated from the diagnostic results based on these realizations. The framework is applied to a scenario mimicking the Beaufort Gyre marginal ice zone, where large uncertainty appears in estimating the ocean field using Lagrangian data assimilation with sparse ice floe trajectories. The skills in counting the number of eddies and computing the probability of each eddy event are significantly improved under the probabilistic framework. Notably, incorporating the nonlinear propagation of uncertainty in diagnostics provides a more accurate mean estimate than standard deterministic methods in estimating eddy lifetime. It also facilitates uncertainty quantification in inferring such a crucial dynamical quantity.

math.DS↗

arXiv2023

Effective Statistical Control Strategies for Complex Turbulent Dynamical Systems

Control of complex turbulent dynamical systems involving strong nonlinearity and high degrees of internal instability is an important topic in practice. Different from traditional methods for controlling individual trajectories, controlling the statistical features of a turbulent system offers a more robust and efficient approach. Crude first-order linear response approximations were typically employed in previous works for statistical control with small initial perturbations. This paper aims to develop two new statistical control strategies for scenarios with more significant initial perturbations and stronger nonlinear responses, allowing the statistical control framework to be applied to a much wider range of problems. First, higher-order methods, incorporating the second-order terms, are developed to resolve the full control-forcing relation. The corresponding changes to recovering the forcing perturbation effectively improve the performance of the statistical control strategy. Second, a mean closure model for the mean response is developed, which is based on the explicit mean dynamics given by the underlying turbulent dynamical system. The dependence of the mean dynamics on higher-order moments is closed using linear response theory but for the response of the second-order moments to the forcing perturbation rather than the mean response directly. The performance of these methods is evaluated extensively on prototype nonlinear test models, which exhibit crucial turbulent features, including non-Gaussian statistics and regime switching with large initial perturbations. The numerical results illustrate the feasibility of different approaches due to their physical and statistical structures and provide detailed guidelines for choosing the most suitable method based on the model properties.

math.DS↗

arXiv2022

Bridging Gaps in the Climate Observation Network: A Physics-based Nonlinear Dynamical Interpolation of Lagrangian Ice Floe Measurements via Data-Driven Stochastic Models

Modeling and understanding sea ice dynamics in marginal ice zones relies on acquiring Lagrangian ice floe measurements. However, optical satellite images are susceptible to atmospheric noise, leading to gaps in the retrieved time series of floe positions. This paper presents an efficient and statistically accurate nonlinear dynamical interpolation framework for recovering missing floe observations. It exploits a balanced physics-based and data-driven construction to address the challenges posed by the high-dimensional and nonlinear nature of the coupled atmosphere-ice-ocean system, where effective reduced-order stochastic models, nonlinear data assimilation, and simultaneous parameter estimation are systematically integrated. The new method succeeds in recovering the locations, curvatures, angular displacements, and the associated strong non-Gaussian distributions of the missing floes in the Beaufort Sea. It also accurately estimates floe thickness and recovers the unobserved underlying ocean field with an appropriate uncertainty quantification, advancing our understanding of Arctic climate.

physics.ao-ph↗