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Parameter estimation for differential equations: a generalized smoothing approach

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Cited by:

  1. Christian Genest & Johanna G. Nešlehová, 2014. "A Conversation with James O. Ramsay," International Statistical Review, International Statistical Institute, vol. 82(2), pages 161-183, August.
  2. J. Cao & L. Wang & J. Xu, 2011. "Robust Estimation for Ordinary Differential Equation Models," Biometrics, The International Biometric Society, vol. 67(4), pages 1305-1313, December.
  3. Hanwen Huang, 2022. "Bayesian multi‐level mixed‐effects model for influenza dynamics," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1978-1995, November.
  4. Jaeger, Jonathan & Lambert, Philippe, 2012. "On the use of adhesion parameters to validate models specified using systems of affine differential equations," LIDAM Discussion Papers ISBA 2012018, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
  5. Pascal Deboeck & Steven Boker, 2010. "Modeling Noisy Data with Differential Equations Using Observed and Expected Matrices," Psychometrika, Springer;The Psychometric Society, vol. 75(3), pages 420-437, September.
  6. Ying Zhu, 2021. "Phase transitions in nonparametric regressions," Papers 2112.03626, arXiv.org, revised Nov 2023.
  7. Laura Azzimonti & Laura M. Sangalli & Piercesare Secchi & Maurizio Domanin & Fabio Nobile, 2015. "Blood Flow Velocity Field Estimation Via Spatial Regression With PDE Penalization," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1057-1071, September.
  8. Hulin Wu & Hongqi Xue & Arun Kumar, 2012. "Numerical Discretization-Based Estimation Methods for Ordinary Differential Equation Models via Penalized Spline Smoothing with Applications in Biomedical Research," Biometrics, The International Biometric Society, vol. 68(2), pages 344-352, June.
  9. Nanshan, Muye & Zhang, Nan & Xun, Xiaolei & Cao, Jiguo, 2022. "Dynamical modeling for non-Gaussian data with high-dimensional sparse ordinary differential equations," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
  10. Fang Yao & Yichao Wu & Jialin Zou, 2016. "Probability-enhanced effective dimension reduction for classifying sparse functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 1-22, March.
  11. Nehla Debbabi & Marie Kratz & Mamadou Mboup, 2016. "A self-calibrating method for heavy tailed data modeling : Application in neuroscience and finance," Working Papers hal-01424298, HAL.
  12. Takanori Hasegawa & Rui Yamaguchi & Masao Nagasaki & Satoru Miyano & Seiya Imoto, 2014. "Inference of Gene Regulatory Networks Incorporating Multi-Source Biological Knowledge via a State Space Model with L1 Regularization," PLOS ONE, Public Library of Science, vol. 9(8), pages 1-19, August.
  13. Qianwen Tan & Subhashis Ghosal, 2021. "Bayesian Analysis of Mixed-effect Regression Models Driven by Ordinary Differential Equations," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 3-29, May.
  14. Baisen Liu & Liangliang Wang & Yunlong Nie & Jiguo Cao, 2021. "Semiparametric Mixed-Effects Ordinary Differential Equation Models with Heavy-Tailed Distributions," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(3), pages 428-445, September.
  15. Nancy Heckman, 2010. "Comments on: Dynamic relations for sparsely sampled Gaussian processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 46-49, May.
  16. Jaeger, Jonathan & Lambert, Philippe, 2012. "Bayesian penalized smoothing approaches in models specified using affine differential equations with unknown error distributions," LIDAM Discussion Papers ISBA 2012017, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
  17. Qiu, Xing & Xu, Tao & Soltanalizadeh, Babak & Wu, Hulin, 2022. "Identifiability analysis of linear ordinary differential equation systems with a single trajectory," Applied Mathematics and Computation, Elsevier, vol. 430(C).
  18. Benham, Tim & Duan, Qibin & Kroese, Dirk P. & Liquet, Benoît, 2017. "CEoptim: Cross-Entropy R Package for Optimization," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 76(i08).
  19. Cao, Jiguo & Ramsay, James O., 2009. "Generalized profiling estimation for global and adaptive penalized spline smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2550-2562, May.
  20. Tao Lu & Yangxin Huang & Min Wang & Feng Qian, 2014. "A refined parameter estimating approach for HIV dynamic model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(8), pages 1645-1657, August.
  21. Shizhe Chen & Ali Shojaie & Daniela M. Witten, 2017. "Network Reconstruction From High-Dimensional Ordinary Differential Equations," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1697-1707, October.
  22. Stephen Tennenbaum & Caroline Freitag & Svetlana Roudenko, 2014. "Modeling the Influence of Environment and Intervention onCholera in Haiti," Mathematics, MDPI, vol. 2(3), pages 1-36, September.
  23. Zhou, Jie & Han, Lu & Liu, Sanyang, 2013. "Nonlinear mixed-effects state space models with applications to HIV dynamics," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1448-1456.
  24. Ahn, Kwang Woo & Chan, Kung-Sik, 2014. "Approximate conditional least squares estimation of a nonlinear state-space model via an unscented Kalman filter," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 243-254.
  25. Hong, Zhaoping & Lian, Heng, 2012. "Time-varying coefficient estimation in differential equation models with noisy time-varying covariates," Journal of Multivariate Analysis, Elsevier, vol. 103(1), pages 58-67, January.
  26. Hooker, Giles & Ramsay, James O. & Xiao, Luo, 2016. "CollocInfer: Collocation Inference in Differential Equation Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 75(i02).
  27. Mu Niu & Benn Macdonald & Simon Rogers & Maurizio Filippone & Dirk Husmeier, 2018. "Statistical inference in mechanistic models: time warping for improved gradient matching," Computational Statistics, Springer, vol. 33(2), pages 1091-1123, June.
  28. Van Kinh Nguyen & Frank Klawonn & Rafael Mikolajczyk & Esteban A Hernandez-Vargas, 2016. "Analysis of Practical Identifiability of a Viral Infection Model," PLOS ONE, Public Library of Science, vol. 11(12), pages 1-16, December.
  29. Gianluca Frasso & Jonathan Jaeger & Philippe Lambert, 2016. "Parameter estimation and inference in dynamic systems described by linear partial differential equations," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(3), pages 259-287, July.
  30. Xinyu Zhang & Jiguo Cao & Raymond J. Carroll, 2015. "On the selection of ordinary differential equation models with application to predator-prey dynamical models," Biometrics, The International Biometric Society, vol. 71(1), pages 131-138, March.
  31. Fang Yao & Yichao Wu & Jialin Zou, 2016. "Probability-enhanced effective dimension reduction for classifying sparse functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 1-22, March.
  32. Xinyu Zhang & Jiguo Cao & Raymond J. Carroll, 2017. "Estimating varying coefficients for partial differential equation models," Biometrics, The International Biometric Society, vol. 73(3), pages 949-959, September.
  33. Laura M. Sangalli & James O. Ramsay & Timothy O. Ramsay, 2013. "Spatial spline regression models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 681-703, September.
  34. Giles Hooker, 2010. "Comments on: Dynamic relations for sparsely sampled Gaussian processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 50-53, May.
  35. Gurami Tsitsiashvili & Alexey Gudimenko & Marina Osipova, 2023. "Fast Method for Estimating the Parameters of Partial Differential Equations from Inaccurate Observations," Mathematics, MDPI, vol. 11(22), pages 1-13, November.
  36. Nehla, Debbabi & Marie, Kratz & Mamadou , Mboup, 2016. "A self-calibrating method for heavy tailed data modeling : Application in neuroscience and finance," ESSEC Working Papers WP1619, ESSEC Research Center, ESSEC Business School.
  37. Mehrdoust, Farshid & Noorani, Idin & Kanniainen, Juho, 2024. "Valuation of option price in commodity markets described by a Markov-switching model: A case study of WTI crude oil market," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 228-269.
  38. Ross, J.V., 2012. "On parameter estimation in population models III: Time-inhomogeneous processes and observation error," Theoretical Population Biology, Elsevier, vol. 82(1), pages 1-17.
  39. Paul Fearnhead & Vasilieos Giagos & Chris Sherlock, 2014. "Inference for reaction networks using the linear noise approximation," Biometrics, The International Biometric Society, vol. 70(2), pages 457-466, June.
  40. Giles Hooker, 2009. "Forcing Function Diagnostics for Nonlinear Dynamics," Biometrics, The International Biometric Society, vol. 65(3), pages 928-936, September.
  41. Sy-Miin Chow & Zhaohua Lu & Andrew Sherwood & Hongtu Zhu, 2016. "Fitting Nonlinear Ordinary Differential Equation Models with Random Effects and Unknown Initial Conditions Using the Stochastic Approximation Expectation–Maximization (SAEM) Algorithm," Psychometrika, Springer;The Psychometric Society, vol. 81(1), pages 102-134, March.
  42. Steffen Borchers & Sandro Bosio & Rolf Findeisen & Utz-Uwe Haus & Philipp Rumschinski & Robert Weismantel, 2011. "Graph problems arising from parameter identification of discrete dynamical systems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 73(3), pages 381-400, June.
  43. Matthew Plumlee & V. Roshan Joseph & Hui Yang, 2016. "Calibrating Functional Parameters in the Ion Channel Models of Cardiac Cells," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 500-509, April.
  44. Sy-Miin Chow & Lu Ou & Arridhana Ciptadi & Emily B. Prince & Dongjun You & Michael D. Hunter & James M. Rehg & Agata Rozga & Daniel S. Messinger, 2018. "Representing Sudden Shifts in Intensive Dyadic Interaction Data Using Differential Equation Models with Regime Switching," Psychometrika, Springer;The Psychometric Society, vol. 83(2), pages 476-510, June.
  45. Arnone, Eleonora & Azzimonti, Laura & Nobile, Fabio & Sangalli, Laura M., 2019. "Modeling spatially dependent functional data via regression with differential regularization," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 275-295.
  46. JAEGER, Jonathan & LAMBERT, Philippe, 2011. "Bayesian generalized profiling estimation in hierarchical linear dynamic systems," LIDAM Discussion Papers ISBA 2011001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
  47. Zhao-Hua Lu & Sy-Miin Chow & Nilam Ram & Pamela M. Cole, 2019. "Zero-Inflated Regime-Switching Stochastic Differential Equation Models for Highly Unbalanced Multivariate, Multi-Subject Time-Series Data," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 611-645, June.
  48. Xifara, T. & Sherlock, C. & Livingstone, S. & Byrne, S. & Girolami, M., 2014. "Langevin diffusions and the Metropolis-adjusted Langevin algorithm," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 14-19.
  49. Golchi, Shirin & Campbell, David A., 2016. "Sequentially Constrained Monte Carlo," Computational Statistics & Data Analysis, Elsevier, vol. 97(C), pages 98-113.
  50. Wei, Baolei, 2022. "Sparse dynamical system identification with simultaneous structural parameters and initial condition estimation," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
  51. Jiguo Cao & Gregor F. Fussmann & James O. Ramsay, 2008. "Estimating a Predator‐Prey Dynamical Model with the Parameter Cascades Method," Biometrics, The International Biometric Society, vol. 64(3), pages 959-967, September.
  52. Liu Baisen & Wang Liangliang & Cao Jiguo, 2018. "Bayesian estimation of ordinary differential equation models when the likelihood has multiple local modes," Monte Carlo Methods and Applications, De Gruyter, vol. 24(2), pages 117-127, June.
  53. Olena Kostylenko & Helena Sofia Rodrigues & Delfim F. M. Torres, 2019. "Parametric identification of the dynamics of inter-sectoral balance: modelling and forecasting," Papers 1904.00029, arXiv.org.
  54. Bernardi, Mara S. & Carey, Michelle & Ramsay, James O. & Sangalli, Laura M., 2018. "Modeling spatial anisotropy via regression with partial differential regularization," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 15-30.
  55. Liu, Baisen & Wang, Liangliang & Nie, Yunlong & Cao, Jiguo, 2019. "Bayesian inference of mixed-effects ordinary differential equations models using heavy-tailed distributions," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 233-246.
  56. Lee, Kyoungjae & Lee, Jaeyong & Dass, Sarat C., 2018. "Inference for differential equation models using relaxation via dynamical systems," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 116-134.
  57. Chen, Yaqing & Dawson, Matthew & Müller, Hans-Georg, 2020. "Rank dynamics for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 149(C).
  58. Zhou, Jie, 2015. "Detection of influential measurement for ordinary differential equation with application to HIV dynamics," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 324-332.
  59. Carey, M. & Ramsay, J.O., 2021. "Fast stable parameter estimation for linear dynamical systems," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
  60. Carey, Michelle & Gath, Eugene G. & Hayes, Kevin, 2014. "Frontiers in financial dynamics," Research in International Business and Finance, Elsevier, vol. 30(C), pages 369-376.
  61. Strebel, Oliver, 2013. "A preprocessing method for parameter estimation in ordinary differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 93-104.
  62. Aguilera, Ana M. & Escabias, Manuel & Valderrama, Mariano J., 2008. "Discussion of different logistic models with functional data. Application to Systemic Lupus Erythematosus," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 151-163, September.
  63. Jonathan Jaeger & Philippe Lambert, 2014. "Bayesian penalized smoothing approaches in models specified using differential equations with unknown error distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(12), pages 2709-2726, December.
  64. Mu Niu & Joe Wandy & Rónán Daly & Simon Rogers & Dirk Husmeier, 2021. "R package for statistical inference in dynamical systems using kernel based gradient matching: KGode," Computational Statistics, Springer, vol. 36(1), pages 715-747, March.
  65. Bin Zhu & Peter X.-K. Song & Jeremy M.G. Taylor, 2011. "Stochastic Functional Data Analysis: A Diffusion Model-Based Approach," Biometrics, The International Biometric Society, vol. 67(4), pages 1295-1304, December.
  66. Quentin Clairon & Adeline Samson, 2022. "Optimal control for parameter estimation in partially observed hypoelliptic stochastic differential equations," Computational Statistics, Springer, vol. 37(5), pages 2471-2491, November.
  67. González Javier & Vujačić Ivan & Wit Ernst, 2013. "Inferring latent gene regulatory network kinetics," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 12(1), pages 109-127, March.
  68. Commenges, D. & Jolly, D. & Drylewicz, J. & Putter, H. & Thiébaut, R., 2011. "Inference in HIV dynamics models via hierarchical likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 446-456, January.
  69. Zhang, Tingting & Sun, Yinge & Li, Huazhang & Yan, Guofen & Tanabe, Seiji & Miao, Ruizhong & Wang, Yaotian & Caffo, Brian S. & Quigg, Mark S., 2020. "Bayesian inference of a directional brain network model for intracranial EEG data," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
  70. Hanwen Huang & Andreas Handel & Xiao Song, 2020. "A Bayesian approach to estimate parameters of ordinary differential equation," Computational Statistics, Springer, vol. 35(3), pages 1481-1499, September.
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