Statistical inference for dynamical systems: A review

McGoff, Kevin; Mukherjee, Sayan; Pillai, Natesh S.

doi:10.1214/15-ss111

Cited by 34 publications

(32 citation statements)

References 180 publications

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“…Parameter estimation appears in many computational problems including model identification , model calibration (Zechner et al, 2011), model discrimination (Kuepfer et al, 2007), model identifiability (Geffen et al, 2008), model checking (Cseke et al, 2016), sensitivity analysis (Erguler and Stumpf, 2011), optimum experiment design (Ruess and Lygeros, 2015), bifurcation analysis (Engl et al, 2009), reachability analysis (Tenazinha and Vinga, 2011), causality analysis (Carmi et al, 2013), stability analysis (Dochain, 2003), network inference (Smet and Marchal, 2010), and control of BRN (Venayak et al, 2018). A survey of parameter estimation methods for chemical reaction systems can be found, for example, in (Gupta, 2013;Baker et al, 2015;Chou and Voit, 2009;McGoff et al, 2015). Other review papers on parameter estimation in BRNs and other dynamic systems are listed in Table 5.…”

Section: Review Of Parameter Estimation Strategies For Brnsmentioning

confidence: 99%

“…(cont.) Kulikov and Kulikova (2015a) Cited by Kulikov and Kulikova (2017) Cited by Kutalik et al (2007) Cited by Kuwahara et al (2013) Cited by Lakatos et al (2015) Cited by Lang and Stelling (2016) Cited by Li and Vu (2013) Cited by Li and Vu (2015) Cited by Liao et al (2015a) Cited by Liao et al (2015b) Cited by Liepe et al (2014) Cited by Lillacci and Khammash (2010a) Cited by Lillacci and Khammash (2010b) Cited by Lillacci and Khammash (2012) Cited by Lindera and Rempala (2015) Cited by Liu et al (2006) Cited by Liu and Wang (2008b) Cited by Liu and Wang (2008a) Cited by Liu and Wang (2009) Cited by Liu et al (2012) Cited by Liu and Gunawan (2014) Cited by Loos et al (2016) Cited by Lück and Wolf (2016) Cited by Mancini et al (2015) Cited by Mannakee et al (2016) Cited by Mansouri et al (2014) Cited by Mansouri et al (2015) Cited by Matsubara et al (2006) Cited by Mazur (2012) Cited by Mazur and Kaderali (2013) Cited by McGoff et al (2015) Cited by Meskin et al (2011) Cited by Meskin et al (2013) Cited by Meyer et al (2014) Cited by Michailidis and dAlché Buc (2013) Cited by Michalik et al (2009) Cited by Mihaylova et al (2011) Cited by Mihaylova et al (2012) Cited by…”

Section: Abdullah Et Al (2013b)mentioning

confidence: 99%

“…Parameter likelihoods can be updated assuming increments and decrements of the species counts (Lecca et al, 2009). Probabilistic state space representation of BRNs as dynamic systems was considered in (Andreychenko et al, 2011;Gupta and Rawlings, 2014;McGoff et al, 2015;Schnoerr et al, 2017). Augmented state space representation of BRN from ordinary differential equations (ODEs) is obtained in (Baker et al, 2013).…”

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confidence: 99%

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Comprehensive Review of Models and Methods for Inferences in Bio-Chemical Reaction Networks

2019

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The key processes in biological and chemical systems are described by networks of chemical reactions. From molecular biology to biotechnology applications, computational models of reaction networks are used extensively to elucidate their non-linear dynamics. The model dynamics are crucially dependent on the parameter values which are often estimated from observations. Over the past decade, the interest in parameter and state estimation in models of (bio-) chemical reaction networks (BRNs) grew considerably. The related inference problems are also encountered in many other tasks including model calibration, discrimination, identifiability, and checking, and optimum experiment design, sensitivity analysis, and bifurcation analysis. The aim of this review paper is to examine the developments in literature to understand what BRN models are commonly used, and for what inference tasks and inference methods. The initial collection of about 700 documents concerning estimation problems in BRNs excluding books and textbooks in computational biology and chemistry were screened to select over 270 research papers and 20 graduate research theses. The paper selection was facilitated by text mining scripts to automate the search for relevant keywords and terms. The outcomes are presented in tables revealing the levels of interest in different inference tasks and methods for given models in the literature as well as the research trends are uncovered. Our findings indicate that many combinations of models, tasks and methods are still relatively unexplored, and there are many new research opportunities to explore combinations that have not been considered—perhaps for good reasons. The most common models of BRNs in literature involve differential equations, Markov processes, mass action kinetics, and state space representations whereas the most common tasks are the parameter inference and model identification. The most common methods in literature are Bayesian analysis, Monte Carlo sampling strategies, and model fitting to data using evolutionary algorithms. The new research problems which cannot be directly deduced from the text mining data are also discussed.

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Section: Review Of Parameter Estimation Strategies For Brnsmentioning

confidence: 99%

Section: Abdullah Et Al (2013b)mentioning

confidence: 99%

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confidence: 99%

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Comprehensive Review of Models and Methods for Inferences in Bio-Chemical Reaction Networks

2019

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“…Whereas it is easy to set up an LV or BST model for a complex biological system in a symbolic format, the identification of optimal parameter values continues to be a significant challenge. As a consequence, estimating parameters of systems of ordinary differential equations (ODEs) remains to be an active research area that attracts contributions from a variety of scientific fields (e.g., Gennemark & Wedelin (2007), Chou & Voit (2009), Girolami & Calderhead (2011), McGoff et al (2015), Ramsay & Hooker (2017), and Schittkowski (2002)). Indeed, numerous optimization methods for ODE models have been proposed in recent years, but none works exceptionally well throughout wide ranges of application.…”

Section: Introductionmentioning

confidence: 99%

Separable Nonlinear Least-Squares Parameter Estimation for Complex Dynamic Systems

2020

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Nonlinear dynamic models are widely used for characterizing functional forms of processes that govern complex biological pathway systems. Over the past decade, validation and further development of these models became possible due to data collected via high-throughput experiments using methods from molecular biology. While these data are very beneficial, they are typically incomplete and noisy, so that inferring parameter values for complex dynamic models is associated with serious computational challenges. Fortunately, many biological systems have embedded linear mathematical features, which may be exploited, thereby improving fits and leading to better convergence of optimization algorithms.In this paper, we explore options of inference for dynamic models using a novel method of separable nonlinear least-squares optimization, and compare its performance to the traditional nonlinear least-squares method. The numerical results from extensive simulations suggest that the proposed approach is at least as accurate as the traditional nonlinear least-squares, but usually superior, while also enjoying a substantial reduction in computational time.

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“…Early interest from the statistical point of view is reflected in the following surveys [6,12,21,22]. For a recent review of this area with many references, see [33]. There has been significant methodological work in the area of statistical inference for dynamical systems (for a…”

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confidence: 99%

Consistency of maximum likelihood estimation for some dynamical systems

McGoff¹,

Mukherjee²,

Nobel³

et al. 2015

Ann. Statist.

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We consider the asymptotic consistency of maximum likelihood parameter estimation for dynamical systems observed with noise. Under suitable conditions on the dynamical systems and the observations, we show that maximum likelihood parameter estimation is consistent. Our proof involves ideas from both information theory and dynamical systems. Furthermore, we show how some well-studied properties of dynamical systems imply the general statistical properties related to maximum likelihood estimation. Finally, we exhibit classical families of dynamical systems for which maximum likelihood estimation is consistent. Examples include shifts of finite type with Gibbs measures and Axiom A attractors with SRB measures.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1259 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

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Statistical inference for dynamical systems: A review

Cited by 34 publications

References 180 publications

Comprehensive Review of Models and Methods for Inferences in Bio-Chemical Reaction Networks

Comprehensive Review of Models and Methods for Inferences in Bio-Chemical Reaction Networks

Separable Nonlinear Least-Squares Parameter Estimation for Complex Dynamic Systems

Consistency of maximum likelihood estimation for some dynamical systems

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