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Álvaro Gajardo

University of California, Davis

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Hans‐Georg Müller

University of California, Davis

Yaqing Chen

Rutgers Sexual and Reproductive Health and Rights

Satarupa Bhattacharjee

University of Florida

Cody Carroll

University of San Francisco

Paromita Dubey

University of Southern California

Kyunghee Han

University of Illinois Chicago

Xiongtao Dai

University of California, Berkeley

Jianing Fan

University of California, Davis

Jane-Ling Wang

University of California, Davis

Pantelis Z. Hadjipantelis

University of California, Davis

Cooperative Institutions

University of California, Davis

University of California, Berkeley

Fuzhou University

Nanjing University of Posts and Telecommunications

Universidad de Los Altos de Chiapas

University of California System

Statistical and Applied Mathematical Sciences Institute

Beijing Institute of Technology

Peking University

Rutgers Sexual and Reproductive Health and Rights

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Time Dynamics of COVID-19

medRxiv (Cold Spring Harbor Laboratory) (2020)

Cody Carroll Satarupa Bhattacharjee Yaqing Chen Paromita Dubey Jianing Fan

We apply tools from functional data analysis to model cumulative trajectories of COVID-19 cases across countries, establishing a framework for quantifying and comparing cases and deaths across countries longitudinally. It emerges that a country's trajectory during an initial first month "priming period" largely determines how the situation unfolds subsequently. We also propose a method for forecasting case counts, which takes advantage of the common, latent information in the entire sample of curves, instead of just the history of a single country. Our framework facilitates to quantify the effects of demographic covariates and social mobility on doubling rates and case fatality rates through a time-varying regression model. Decreased workplace mobility is associated with lower doubling rates with a roughly two week delay, and case fatality rates exhibit a positive feedback pattern.

Case fatality rate

Sample (material)

10.1101/2020.05.21.20109405

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Citations (3)

Learning delay dynamics for multivariate stochastic processes, with application to the prediction of the growth rate of COVID-19 cases in the United States

Journal of Mathematical Analysis and Applications (2021)

Paromita Dubey Yaqing Chen Álvaro Gajardo Satarupa Bhattacharjee Cody Carroll

Delay differential equation

Pooling

10.1016/j.jmaa.2021.125677

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Citations (1)

Cox Point Process Regression

IEEE Transactions on Information Theory (2021)

Álvaro Gajardo Hans‐Georg Müller

Point processes in time have a wide range of applications that include the claims arrival process in insurance or the analysis of queues in operations research. Due to advances in technology, such samples of point processes are increasingly encountered. A key object of interest is the local intensity function. It has a straightforward interpretation that allows to understand and explore point process data. We consider functional approaches for point processes, where one has a sample of repeated realizations of the point process. This situation is inherently connected with Cox processes, where the intensity functions of the replications are modeled as random functions. Here we study a situation where one records covariates for each replication of the process, such as the daily temperature for bike rentals. For modeling point processes as responses with vector covariates as predictors we propose a novel regression approach for the intensity function that is intrinsically nonparametric. While the intensity function of a point process that is only observed once on a fixed domain cannot be identified, we show how covariates and repeated observations of the process can be utilized to make consistent estimation possible, and we also derive asymptotic rates of convergence without invoking parametric assumptions.

Cox process

10.1109/tit.2021.3126466

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Citations (5)

Distributional Representation of Longitudinal Data: Visualization, Regression and Prediction

arXiv (Cornell University) (2021)

Álvaro Gajardo Xiongtao Dai Hans‐Georg Müller

We develop a representation of Gaussian distributed sparsely sampled longitudinal data whereby the data for each subject are mapped to a multivariate Gaussian distribution; this map is entirely data-driven. The proposed method utilizes functional principal component analysis and is nonparametric, assuming no prior knowledge of the covariance or mean structure of the longitudinal data. This approach naturally connects with a deeper investigation of the behavior of the functional principal component scores obtained for longitudinal data, as the number of observations per subject increases from sparse to dense. We show how this is reflected in the shrinkage of the distribution of the conditional scores given noisy longitudinal observations towards a point mass located at the true but unobservable FPCs. Mapping each subject's sparse observations to the corresponding conditional score distribution leads to useful visualizations and representations of sparse longitudinal data. Asymptotic rates of convergence as sample size increases are obtained for the 2-Wasserstein metric between the true and estimated conditional score distributions, both for a $K$-truncated functional principal component representation as well as for the case when $K=K(n)$ diverges with sample size $n\to\infty$. We apply these ideas to construct predictive distributions aimed at predicting outcomes given sparse longitudinal data.

Conditional probability distribution

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Cox Point Process Regression

arXiv (Cornell University) (2020)

Álvaro Gajardo Hans‐Georg Müller

Cox process

10.48550/arxiv.2006.00447

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Functional Data Analysis and Empirical Dynamics [R package fdapace version 0.5.8]

Álvaro Gajardo Satarupa Bhattacharjee Cody Carroll Yaqing Chen Xiongtao Dai

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Point process models for COVID-19 cases and deaths

Journal of Applied Statistics (2021)

Álvaro Gajardo Hans‐Georg Müller

The study of events distributed over time which can be quantified as point processes has attracted much interest over the years due to its wide range of applications. It has recently gained new relevance due to the COVID-19 case and death processes associated with SARS-CoV-2 that characterize the COVID-19 pandemic and are observed across different countries. It is of interest to study the behavior of these point processes and how they may be related to covariates such as mobility restrictions, gross domestic product per capita, and fraction of population of older age. As infections and deaths in a region are intrinsically events that arrive at random times, a point process approach is natural for this setting. We adopt techniques for conditional functional point processes that target point processes as responses with vector covariates as predictors, to study the interaction and optimal transport between case and death processes and doubling times conditional on covariates.

Time point

Pandemic

Relevance

10.1080/02664763.2021.1907839

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Citations (6)

Time dynamics of COVID-19

Scientific Reports (2020)

Cody Carroll Satarupa Bhattacharjee Yaqing Chen Paromita Dubey Jianing Fan

Abstract We apply tools from functional data analysis to model cumulative trajectories of COVID-19 cases across countries, establishing a framework for quantifying and comparing cases and deaths across countries longitudinally. It emerges that a country’s trajectory during an initial first month “priming period” largely determines how the situation unfolds subsequently. We also propose a method for forecasting case counts, which takes advantage of the common, latent information in the entire sample of curves, instead of just the history of a single country. Our framework facilitates to quantify the effects of demographic covariates and social mobility on doubling rates and case fatality rates through a time-varying regression model. Decreased workplace mobility is associated with lower doubling rates with a roughly 2 week delay, and case fatality rates exhibit a positive feedback pattern.

Case fatality rate

Sample (material)

2019-20 coronavirus outbreak

10.1038/s41598-020-77709-4

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Citations (43)

Statistical Analysis for Random Objects and Non-Euclidean Data [R package frechet version 0.2.0]

Yaqing Chen Álvaro Gajardo Jianing Fan Qixian Zhong Paromita Dubey

Statistical Analysis

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Citations (1)

Learning delay dynamics for multivariate stochastic processes, with application to the prediction of the growth rate of COVID-19 cases in the United States

arXiv (Cornell University) (2021)

Paromita Dubey Yaqing Chen Álvaro Gajardo Satarupa Bhattacharjee Cody Carroll

Delay differential equations form the underpinning of many complex dynamical systems. The forward problem of solving random differential equations with delay has received increasing attention in recent years. Motivated by the challenge to predict the COVID-19 caseload trajectories for individual states in the U.S., we target here the inverse problem. Given a sample of observed random trajectories obeying an unknown random differential equation model with delay, we use a functional data analysis framework to learn the model parameters that govern the underlying dynamics from the data. We show existence and uniqueness of the analytical solutions of the population delay random differential equation model when one has discrete time delays in the functional concurrent regression model and also for a second scenario where one has a delay continuum or distributed delay. The latter involves a functional linear regression model with history index. The derivative of the process of interest is modeled using the process itself as predictor and also other functional predictors with predictor-specific delayed impacts. This dynamics learning approach is shown to be well suited to model the growth rate of COVID-19 for the states that are part of the U.S., by pooling information from the individual states, using the case process and concurrently observed economic and mobility data as predictors.

Delay differential equation

Pooling

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