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This paper presents a modeling framework---mathematical model and computational framework---to study the response of a plastic material due to the presence and transport of a chemical species in the host material. Such a modeling framework…
Periodic patterns in dynamical behaviours of biological models described by simple form differential delay equations are studied. Mathematical models are given by a class of scalar delay differential equations with a multiplicative time…
It is important to accurately model materials' properties at lower length scales (micro-level) while translating the effects to the components and/or system level (macro-level) can significantly reduce the amount of experimentation required…
Changes in the timescales at which complex systems evolve are essential to predicting critical transitions and catastrophic failures. Disentangling the timescales of the dynamics governing complex systems remains a key challenge. With this…
In many practices, scientists are particularly interested in detecting which of the predictors are truly associated with a multivariate response. It is more accurate to model multiple responses as one vector rather than separating each…
We develop the methodology and a detailed case study in use of a class of Bayesian predictive synthesis (BPS) models for multivariate time series forecasting. This extends the recently introduced foundational framework of BPS to the…
Mixed modeling of extreme values and random effects is relatively unexplored topic. Computational difficulties in using the maximum likelihood method for mixed models and the fact that maximum likelihood method uses available data and does…
High-dimensional variable selection, with many more covariates than observations, is widely documented in standard regression models, but there are still few tools to address it in non-linear mixed-effects models where data are collected…
We consider the problem of multivariate density deconvolution where the distribution of a random vector needs to be estimated from replicates contaminated with conditionally heteroscedastic measurement errors. We propose a conceptually…
This paper presents a novel centralized, variational data assimilation approach for calibrating transient dynamic models in electrical power systems, focusing on load model parameters. With the increasing importance of inverter-based…
In many environmental applications involving spatially-referenced data, limitations on the number and locations of observations motivate the need for practical and efficient models for spatial interpolation, or kriging. A key component of…
Many real-world scientific processes are governed by complex nonlinear dynamic systems that can be represented by differential equations. Recently, there has been increased interest in learning, or discovering, the forms of the equations…
Parameter identification and comparison of dynamical systems is a challenging task in many fields. Bayesian approaches based on Gaussian process regression over time-series data have been successfully applied to infer the parameters of a…
Assessing the degradation state of an industrial asset first requires evaluating its current condition and then to project the forecast model trajectory to a predefined prognostic threshold, thereby estimating its remaining useful life…
Network models provide a powerful framework for analysing single-cell count data, facilitating the characterisation of cellular identities, disease mechanisms, and developmental trajectories. However, uncertainty modeling in unsupervised…
This paper develops a framework for creating damage accumulation models for engineered wood products by invoking the classical theory of non--dimensionalization. The result is a general class of such models. Both the US and Canadian damage…
One of the major research questions regarding human microbiome studies is the feasibility of designing interventions that modulate the composition of the microbiome to promote health and cure disease. This requires extensive understanding…
A data driven finite element method (DDFEM) that accounts for more than two material state variables has been presented in this work. DDFEM framework is motivated from (1,2) and can account for multiple state variables, viz. stresses,…
Ecological Momentary Assessments (EMA) capture real-time thoughts and behaviors in natural settings, producing rich longitudinal data for statistical and physiological analyses. However, the robustness of these analyses can be compromised…
Dynamical system state estimation and parameter calibration problems are ubiquitous across science and engineering. Bayesian approaches to the problem are the gold standard as they allow for the quantification of uncertainties and enable…