Parameter estimation for differential equations: a generalized smoothing approach

By James O. Ramsay, Giles Hooker, David Alexander Campbell, Jiguo Cao. 2007

713 citations recorded by the source corpus.

Subfields: Control and Systems Engineering

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Citations in the corpus

Causal Models for Dynamical Systems (2020, methodology): “…of goodness-of-ﬁt of the integrated system, nonlinear least squares methods or gradient matching [Bard, 1974, Benson, 1979, Calderhead et al., 2009, Varah, 1982, Ramsay et al., 2007, Macdonald and Husmeier, 2015, Dattner and Klaassen, 2015, Raue et al., 2015, Oates et al., 2014, Wenk et al., 2019].”
Langevin diffusions and the Metropolis-adjusted Langevin algorithm (2013, neutral): “We now consider the FitzHugh–Nagumo differential equations in Ramsay et al. (2007): Ẇ = c ( W −W 3/3 +R ) and Ṙ = −(W − a + bT )/c.”
Network Reconstruction From High-Dimensional Ordinary Differential Equations (2016, methodology): “tep collocation methods In order to overcome the computational challenges associated with solving (3), collocation methods have been employed by a number of authors (Varah, 1982; Ellner et al., 2002; Ramsay et al., 2007; Brunel, 2008; Cao and Zhao, 2008; Liang and Wu, 2008; Cao et al., 2011; Lu et a”
Learning Large Scale Ordinary Differential Equation Systems (2017, methodology): “…xl(0)−∑ j,k Ψk(x̂j)(t)θljk 2, with Ψk(x)(t) := ∫ t 0 ψk(x(s)) ds. Note that both nonparametric methods assume f to be additive in the coordinates of x. Finally, we note that the generalised profiling method described by Ramsay et al. (2007) is another variation on the inverse collocation method.”
Zero Variance Differential Geometric Markov Chain Monte Carlo Algorithms (2014, methodology): “As an example of ZV-RMHMC and ZV-MMALA under an ODE model, consider the Fitzhugh-Nagumo ODEs (see for example Ramsay et al. (2007))”
Gradient Matching Methods for Computational Inference in Mechanistic Models for Systems Biology: A Review and Comparative Analysis (2015, methodology): “…González et al. (2013), who implement a reproducing kernel Hilbert space (RKHS) and penalized maximum likelihood approach in a non-Bayesian fashion; Ramsay et al. (2007), who optimize the gradient mismatch, interpolant, and ODE parameters using a hierarchical regularization method and penalize the…”
Magnetic Hamiltonian Monte Carlo (2016, methodology): “0 to generate 200 evenlyspaced noise-corrupted observations over the time interval t = [0, 20] (as in (Ramsay et al., 2007; Girolami & Calderhead, 2011)).”
Estimating Derivatives for Samples of Sparsely Observed Functions, With Application to Online Auction Dynamics (2009, background): “Recent and ongoing work is establishing connections with the solutions of differential equations for densely observed functional data (Ramsay et al. 2007) and also with longitudinal data analysis.”
Bayesian Solution Uncertainty Quantification for Differential Equations (2013, background): “…problem concerns the uncertainty in unknown model inputs, θ , given measurements of the model states (Bock, 1983; Ionides et al., 2006; Dowd, 2007; Ramsay et al., 2007; Xue et al., 2010; Brunel, 2008; Liang and Wu, 2008; Calderhead and Girolami, 2011; Campbell and Steele, 2011; Gugushvili and…”
Twenty years of P-splines (2015, methodology): “One can write the solution as a sum of B-splines (the collocation method) and use the differential equation (DE) as the penalty (Ramsay et al., 2007).”
Sparse Additive Ordinary Differential Equations for Dynamic Gene Regulatory Network Modeling (2014, methodology): “Some other more efﬁcient estimation approaches for ODE models such as the numerical discretization-based estimation method (Wu, Xue, and Kumar 2012) and generalized proﬁling approach (Ramsay et al. 2007) may also be considered for high-dimensional ODE variable selection.”
Mechanistic Hierarchical Gaussian Processes (2014, methodology): “thors (Ramsay et al. 2007; Calderhead, Girolami, and Lawrence 2009) developed novel techniques for estimating nonlinear differential equations using smoothing-based approximations.”
√n-consistent parameter estimation for systems of ordinary differential equations : bypassing numerical integration via smoothing (2010, neutral): “There exists an alternative approach to the ones described here, which also employs nonparametric smoothing, see Ramsay et al. (2007).”