Bayesian inference of high-dimensional, cluster-structured ordinary differential equation models with applications to brain connectivity studies

Zhang, Tingting; Yin, Qiannan; Caffo, Brian; Sun, Yinge; Boatman-Reich, Dana

doi:10.1214/17-aoas1021

Cited by 18 publications

(8 citation statements)

References 73 publications

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“…Because of the uncertainty resulted from the high-dimensionality, posterior probabilities P m ij and P γ ij are all small. To address this issue, many Bayesian methods select variables based on the ranks of their posterior probabilities [21,50]. We here propose to determine the thresholds for P m ij and P γ ij based on their significance/p-values under the null hypothesis that all the regions are independent from each other, as explained in detail below.…”

Section: Choice Of Thresholdsmentioning

confidence: 99%

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A Bayesian State-Space Approach to Mapping Directional Brain Networks

Wang

Gao

et al. 2020

Preprint

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Section: Choice Of Thresholdsmentioning

confidence: 99%

“…To address this limitation, [20][21][22] proposed to use linear ODEs to approximate highdimensional brain systems (consisting of many regions). However, parameter estimation of deterministic ODE models is sensitive to the model specification, data noise, and data-sampling frequency.…”

Section: Introductionmentioning

confidence: 99%

A Bayesian State-Space Approach to Mapping Directional Brain Networks

Wang

Gao

et al. 2020

Preprint

Self Cite

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“…This idea originates from parallel tempering and model based smoothing. Zhang et al (2017) proposed a high dimensional linear ordinary differential equation (ODE) model to accommodate the directional interaction in brain areas.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Semiparametric Bayesian Differential Equations Via Sequential Monte Carlo

Wang

Doig

et al. 2021

Journal of Computational and Graphical Statistics

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Nonlinear differential equations (DEs) are used in a wide range of scientific problems to model complex dynamic systems. The differential equations often contain unknown parameters that are of scientific interest, which have to be estimated from noisy measurements of the dynamic system. Generally, there is no closed-form solution for nonlinear DEs, and the likelihood surface for the parameter of interest is multi-modal and very sensitive to different parameter values. We propose a fully Bayesian framework for nonlinear DEs system. A flexible nonparametric function is used to represent the dynamic process such that expensive numerical solvers can be avoided. A sequential Monte Carlo in the annealing framework is proposed to conduct Bayesian inference for parameters in DEs. In our numerical experiments, we use examples of ordinary differential equations and delay differential equations to demonstrate the effectiveness of the proposed algorithm. We developed an R package that is available at https://github.com/shijiaw/smcDE.

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“…Ordinary differential equations (ODE) have been widely used to model dynamic systems and biological and physical processes in a variety of scientific applications. Examples include infectious disease (Liang and Wu, 2008), genomics (Cao and Zhao, 2008;Chou and Voit, 2009;Ma et al, 2009;Lu et al, 2011;Henderson and Michailidis, 2014;Wu et al, 2014), neuroscience (Izhikevich, 2007;Zhang et al, 2015Zhang et al, , 2017Cao et al, 2019), among many others. A system of ODEs takes the form,…”

Section: Introductionmentioning

confidence: 99%

Kernel Ordinary Differential Equations

Dai¹,

Li²

2020

Preprint

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Ordinary differential equations (ODE) are widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernelbased approach for estimation and inference of ODEs given the noisy observations. We do not restrict the functional forms in ODE to be linear or additive, and we allow pairwise interactions. We perform sparse estimation to select individual functionals, and construct confidence intervals for the estimated signal trajectories. We establish the estimation optimality and selection consistency of kernel ODE under both the lowdimensional and high-dimensional settings, where the number of unknown functionals can be smaller or larger than the sample size. Our proposal builds upon the smoothing spline analysis of variance (SS-ANOVA) framework, but tackles several important problems that are not yet fully addressed, and thus extends the scope of existing SS-ANOVA too. We demonstrate the efficacy of our method through numerous ODE examples.

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Bayesian inference of high-dimensional, cluster-structured ordinary differential equation models with applications to brain connectivity studies

Cited by 18 publications

References 73 publications

A Bayesian State-Space Approach to Mapping Directional Brain Networks

A Bayesian State-Space Approach to Mapping Directional Brain Networks

Adaptive Semiparametric Bayesian Differential Equations Via Sequential Monte Carlo

Kernel Ordinary Differential Equations

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