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Son D, Kim J. Estimation of Ordinary Differential Equation Models for Gene Regulatory Networks Through Data Cloning. J Comput Biol 2023; 30:609-618. [PMID: 36898058 DOI: 10.1089/cmb.2022.0201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/12/2023] Open
Abstract
Ordinary differential equations (ODEs) are widely used for elucidating dynamic processes in various fields. One of the applications of ODEs is to describe dynamics of gene regulatory networks (GRNs), which is a critical step in understanding disease mechanisms. However, estimation of ODE models for GRNs is challenging because of inflexibility of the model and noisy data with complex error structures such as heteroscedasticity, correlations between genes, and time dependency. In addition, either a likelihood or Bayesian approach is commonly used for estimation of ODE models, but both approaches have benefits and drawbacks in their own right. Data cloning is a maximum likelihood (ML) estimation method through the Bayesian framework. Since it works in the Bayesian framework, it is free from local optimum problems that are common drawbacks of ML methods. Also, its inference is invariant for the selection of prior distributions, which is a major issue in Bayesian methods. This study proposes an estimation method of ODE models for GRNs through data cloning. The proposed method is demonstrated through simulation and it is applied to real gene expression time-course data.
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Affiliation(s)
- Donghui Son
- Department of Statistics, Sungkyunkwan University, Seoul, South Korea
| | - Jaejik Kim
- Department of Statistics, Sungkyunkwan University, Seoul, South Korea
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2
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Bhaumik P, Shi W, Ghosal S. Two-step Bayesian methods for generalized regression driven by partial differential equations. BERNOULLI 2022. [DOI: 10.3150/21-bej1363] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Prithwish Bhaumik
- Department of Statistics, North Carolina State University, 2311 Stinson Drive, Raleigh, North Carolina 27695-8203, USA
| | - Wenli Shi
- Department of Statistics, North Carolina State University, 2311 Stinson Drive, Raleigh, North Carolina 27695-8203, USA
| | - Subhashis Ghosal
- Department of Statistics, North Carolina State University, 2311 Stinson Drive, Raleigh, North Carolina 27695-8203, USA
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Chakraborty M, Ghosal S. Rates and coverage for monotone densities using projection-posterior. BERNOULLI 2022. [DOI: 10.3150/21-bej1379] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Moumita Chakraborty
- Department of Statistics, North Carolina State University, 2311 Stinson Drive, Raleigh, North Carolina 27695-8203, USA
| | - Subhashis Ghosal
- Department of Statistics, North Carolina State University, 2311 Stinson Drive, Raleigh, North Carolina 27695-8203, USA
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Wang S, Ge S, Doig R, Wang L. Adaptive Semiparametric Bayesian Differential Equations Via Sequential Monte Carlo. J Comput Graph Stat 2021. [DOI: 10.1080/10618600.2021.1987252] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Shijia Wang
- School of Statistics and Data Science, LPMC & KLMDASR, Nankai University, Tianjin, China
| | - Shufei Ge
- Institute of Mathematical Sciences, ShanghaiTech University, Shanghai, China
| | - Renny Doig
- Department of Statistics and Actuarial Science, Simon Fraser University, Burnaby, BC, Canada
| | - Liangliang Wang
- Department of Statistics and Actuarial Science, Simon Fraser University, Burnaby, BC, Canada
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Semiparametric Mixed-Effects Ordinary Differential Equation Models with Heavy-Tailed Distributions. JOURNAL OF AGRICULTURAL, BIOLOGICAL AND ENVIRONMENTAL STATISTICS 2021; 26:428-445. [PMID: 33840991 PMCID: PMC8020077 DOI: 10.1007/s13253-021-00446-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/03/2019] [Revised: 02/12/2021] [Accepted: 02/24/2021] [Indexed: 11/01/2022]
Abstract
Ordinary differential equation (ODE) models are popularly used to describe complex dynamical systems. When estimating ODE parameters from noisy data, a common distribution assumption is using the Gaussian distribution. It is known that the Gaussian distribution is not robust when abnormal data exist. In this article, we develop a hierarchical semiparametric mixed-effects ODE model for longitudinal data under the Bayesian framework. For robust inference on ODE parameters, we consider a class of heavy-tailed distributions to model the random effects of ODE parameters and observations errors. An MCMC method is proposed to sample ODE parameters from the posterior distributions. Our proposed method is illustrated by studying a gene regulation experiment. Simulation studies show that our proposed method provides satisfactory results for the semiparametric mixed-effects ODE models with finite samples. Supplementary materials accompanying this paper appear online.
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Bayesian Analysis of Mixed-effect Regression Models Driven by Ordinary Differential Equations. SANKHYA B 2021. [DOI: 10.1007/s13571-019-00199-6] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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Chakraborty M, Ghosal S. Coverage of credible intervals in nonparametric monotone regression. Ann Stat 2021. [DOI: 10.1214/20-aos1989] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Chakraborty M, Ghosal S. Convergence rates for Bayesian estimation and testing in monotone regression. Electron J Stat 2021. [DOI: 10.1214/21-ejs1861] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Moumita Chakraborty
- Department of Statistics, North Carolina State University, Raleigh, NC 27695, U.S.A
| | - Subhashis Ghosal
- Department of Statistics, North Carolina State University, Raleigh, NC 27695, U.S.A
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Ranciati S, Wit EC, Viroli C. Bayesian smooth‐and‐match inference for ordinary differential equations models linear in the parameters. STAT NEERL 2020. [DOI: 10.1111/stan.12192] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
Affiliation(s)
- Saverio Ranciati
- Department of Statistical SciencesUniversity of Bologna Bologna Italy
| | - Ernst C. Wit
- Institute of Computational ScienceUniversità della Svizzera Italiana Lugano Switzerland
| | - Cinzia Viroli
- Department of Statistical SciencesUniversity of Bologna Bologna Italy
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10
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Huang H, Handel A, Song X. A Bayesian approach to estimate parameters of ordinary differential equation. Comput Stat 2020. [DOI: 10.1007/s00180-020-00962-8] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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11
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Abstract
In this paper, we consider the inverse problem of derivative order estimation in a fractional logistic model. In order to solve the direct problem, we use the Grünwald-Letnikov fractional derivative, then the inverse problem is tackled within a Bayesian perspective. To construct the likelihood function, we propose an explicit numerical scheme based on the truncated series of the derivative definition. By MCMC samples of the marginal posterior distributions, we estimate the order of the derivative and the growth rate parameter in the dynamic model, as well as the noise in the observations. To evaluate the methodology, a simulation was performed using synthetic data, where the bias and mean square error are calculated, the results give evidence of the effectiveness for the method and the suitable performance of the proposed model. Moreover, an example with real data is presented as evidence of the relevance of using a fractional model.
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Liu B, Wang L, Nie Y, Cao J. Bayesian inference of mixed-effects ordinary differential equations models using heavy-tailed distributions. Comput Stat Data Anal 2019. [DOI: 10.1016/j.csda.2019.03.001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Cao X, Sandstede B, Luo X. A Functional Data Method for Causal Dynamic Network Modeling of Task-Related fMRI. Front Neurosci 2019; 13:127. [PMID: 30872989 PMCID: PMC6402339 DOI: 10.3389/fnins.2019.00127] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2018] [Accepted: 02/05/2019] [Indexed: 01/15/2023] Open
Abstract
Functional MRI (fMRI) is a popular approach to investigate brain connections and activations when human subjects perform tasks. Because fMRI measures the indirect and convoluted signals of brain activities at a lower temporal resolution, complex differential equation modeling methods (e.g., Dynamic Causal Modeling) are usually employed to infer the neuronal processes and to fit the resulting fMRI signals. However, this modeling strategy is computationally expensive and remains to be mostly a confirmatory or hypothesis-driven approach. One major statistical challenge here is to infer, in a data-driven fashion, the underlying differential equation models from fMRI data. In this paper, we propose a causal dynamic network (CDN) method to estimate brain activations and connections simultaneously. Our method links the observed fMRI data with the latent neuronal states modeled by an ordinary differential equation (ODE) model. Using the basis function expansion approach in functional data analysis, we develop an optimization-based criterion that combines data-fitting errors and ODE fitting errors. We also develop and implement a block coordinate-descent algorithm to compute the ODE parameters efficiently. We illustrate the numerical advantages of our approach using data from realistic simulations and two task-related fMRI experiments. Compared with various effective connectivity methods, our method achieves higher estimation accuracy while improving the computational speed by from tens to thousands of times. Though our method is developed for task-related fMRI, we also demonstrate the potential applicability of our method (with a simple modification) to resting-state fMRI, by analyzing both simulated and real data from medium-sized networks.
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Affiliation(s)
- Xuefei Cao
- Division of Applied Mathematics, Brown University, Providence, RI, United States
| | - Björn Sandstede
- Division of Applied Mathematics, Brown University, Providence, RI, United States
| | - Xi Luo
- Department of Biostatistics and Data Science, School of Public Health, The University of Texas Health Science Center at Houston, Houston, TX, United States
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Bhaumik P, Ghosal S. Efficient Bayesian estimation and uncertainty quantification in ordinary differential equation models. BERNOULLI 2017. [DOI: 10.3150/16-bej856] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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