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Recent studies demonstrate that trends in indicators extracted from measured time series can indicate approaching to an impending transition. Kendall's {\tau} coefficient is often used to study the trend of statistics related to the…
We propose an informal test for stationarity in a time series which checks for the compatibility of nonlinear approximations to the dynamics made in different segments of the sequence. The segments are compared directly, rather than via…
Nonlinear systems are capable of displaying complex behavior even if this is the result of a small number of interacting time scales. A widely studied case is when complex dynamics emerges out of a nonlinear system being forced by a simple…
Factor analysis models are widely utilized in social and behavioral sciences, such as psychology, education, and marketing, to measure unobservable latent traits. In this article, we introduce a nonlinear structured latent factor analysis…
Joint models for a wide class of response variables and longitudinal measurements consist on a mixed-effects model to fit longitudinal trajectories whose random effects enter as covariates in a generalized linear model for the primary…
We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…
The complexity of mathematical models describing respiratory mechanics has grown in recent years, however, parameter identifiability of such models has only been studied in the last decade in the context of observable data. This study…
Psychiatric questionnaires are highly context sensitive and often only weakly predict subsequent symptom severity, which makes the prognostic relationship difficult to learn. Although flexible nonlinear models can improve predictive…
The method of surrogate data provides a framework for testing observed data against a hierarchy of alternative hypotheses. The aim of applying this method is to exclude the possibility that the data are consistent with simple linear…
Nonlinear regression analysis is a popular and important tool for scientists and engineers. In this article, we introduce theories and methods of nonlinear regression and its statistical inferences using the frequentist and Bayesian…
Count outcomes in longitudinal studies are frequent in clinical and engineering studies. In frequentist and Bayesian statistical analysis, methods such as Mixed linear models allow the variability or correlation within individuals to be…
Natural systems are typically nonlinear and complex, and it is of great interest to be able to reconstruct a system in order to understand its mechanism, which can not only recover nonlinear behaviors but also predict future dynamics. Due…
Monitoring maternal and fetal health during pregnancy is crucial for preventing adverse outcomes. While tests such as ultrasound scans offer high accuracy, they can be costly and inconvenient. Telehealth and more accessible body shape…
Most machine learning techniques are based upon statistical learning theory, often simplified for the sake of computing speed. This paper is focused on the uncertainty aspect of mathematical modeling in machine learning. Regression analysis…
Nonlinear dynamic models are widely used for characterizing functional forms of processes that govern complex biological pathway systems. Over the past decade, validation and further development of these models became possible due to data…
A nonlinear model relating the imposed motion of a circular cylinder, submerged in a fluid flow, to the transverse force coefficient is presented. The nonlinear fluid system, featuring vortex shedding patterns, limit cycle oscillations and…
In this paper an approach to modelling nonstationary binary sequences, i.e., predicting the probability of upcoming symbols, is presented. After studying the prediction model we evaluate its performance in two non-artificial test cases.…
This paper proposes a Bayesian hierarchical model to characterize the relationship between birth weight and maternal pre-eclampsia across gestation at a large maternity hospital in urban Uganda. Key scientific questions we investigate…
Stochastic kinetic models are often used to describe complex biological processes. Typically these models are analytically intractable and have unknown parameters which need to be estimated from observed data. Ideally we would have…
Nonlinear Bayesian update for a prior ensemble is proposed to extend traditional ensemble Kalman filtering to settings characterized by non-Gaussian priors and nonlinear measurement operators. In this framework, the observed component is…