Related papers: Nonparametric modeling and spatiotemporal dynamica…
We present a Bayesian dynamical inference method for characterizing cardiorespiratory (CR) dynamics in humans by inverse modelling from blood pressure time-series data. This new method is applicable to a broad range of stochastic dynamical…
Inference on unknown quantities in dynamical systems via observational data is essential for providing meaningful insight, furnishing accurate predictions, enabling robust control, and establishing appropriate designs for future…
Semiparametric regression offers a flexible framework for modeling non-linear relationships between a response and covariates. A prime example are generalized additive models where splines (say) are used to approximate non-linear functional…
We consider dynamical systems evolving near an equilibrium statistical state where the interest is in modelling long term behavior that is consistent with thermodynamic constraints. We adjust the distribution using an entropy-optimizing…
We introduce a data-based approach to estimating key quantities which arise in the study of nonlinear control systems and random nonlinear dynamical systems. Our approach hinges on the observation that much of the existing linear theory may…
One of the pivotal tasks in scientific machine learning is to represent underlying dynamical systems from time series data. Many methods for such dynamics learning explicitly require the derivatives of state data, which are not directly…
The fundamental lemma from behavioral systems theory yields a data-driven non-parametric system representation that has shown great potential for the data-efficient control of unknown linear and weakly nonlinear systems, even in the…
Parameter estimation of nonlinear state-space models from input-output data typically requires solving a highly non-convex optimization problem prone to slow convergence and suboptimal solutions. This work improves the reliability and…
Conditional copulas are flexible statistical tools that couple joint conditional and marginal conditional distributions. In a linear regression setting with more than one covariate and two dependent outcomes, we propose the use of additive…
In a recent paper Birke and Bissantz (2008) considered the problem of nonparametric estimation in inverse regression models with convolution-type operators. For multivariate predictors nonparametric methods suffer from the curse of…
The case-control sampling design serves as a pivotal strategy in mitigating the imbalanced structure observed in binary data. We consider the estimation of a non-parametric logistic model with the case-control data supplemented by external…
Gaussian processes (GPs) are commonplace in spatial statistics. Although many non-stationary models have been developed, there is arguably a lack of flexibility compared to equipping each location with its own parameters. However, the…
We introduce a novel procedure that, given sparse data generated from a stationary deterministic nonlinear dynamical system, can characterize specific local and/or global dynamic behavior with rigorous probability guarantees. More…
Nonlinear dynamics and pattern formation in the systems with quadratic nonlinearity is computed symbolically by specially developed MATHEMATICA package. A Web interface for the presented methods is developed, which turns the implementations…
Solution of Ordinary Differential Equation (ODE) model of dynamical system may not agree with its observed values. Often this discrepancy can be attributed to unmodeled forcings in the evolution rule of the dynamical system. In this…
We consider the problem of constructing nonparametric undirected graphical models for high-dimensional functional data. Most existing statistical methods in this context assume either a Gaussian distribution on the vertices or linear…
High-fidelity numerical simulations of chaotic, high dimensional nonlinear dynamical systems are computationally expensive, necessitating the development of efficient surrogate models. Most surrogate models for such systems are…
Logistic models are studied as a tool to convert output from numerical weather forecasting systems (deterministic and ensemble) into probability forecasts for binary events. A logistic model obtains by putting the logarithmic odds ratio…
Ordinary differential equations have been used to model dynamical systems in a broad range. Model checking for parametric ordinary differential equations is a necessary step to check whether the assumed models are plausible. In this paper…
We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…