Generalized method of moments for estimating parameters of stochastic reaction networks

Lück, Alexander; Wolf, Verena

doi:10.1186/s12918-016-0342-8

Cited by 29 publications

(19 citation statements)

References 55 publications

(86 reference statements)

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“…Of course, this estimator can also be extended to include information about higher-order moments than two by changing the upper limit of the sum over k . The MLE estimator here used can be seen as a special case of the generalized method of moments estimator used in [42].…”

Section: Methodsmentioning

confidence: 99%

Accuracy of parameter estimation for auto-regulatory transcriptional feedback loops from noisy data

Cao

Grima

2019

J. R. Soc. Interface.

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Bayesian and non-Bayesian moment-based inference methods are commonly used to estimate the parameters defining stochastic models of gene regulatory networks from noisy single cell or population snapshot data. However, a systematic investigation of the accuracy of the predictions of these methods remains missing. Here, we present the results of such a study using synthetic noisy data of a negative auto-regulatory transcriptional feedback loop, one of the most common building blocks of complex gene regulatory networks. We study the error in parameter estimation as a function of (i) number of cells in each sample; (ii) the number of time points; (iii) the highest-order moment of protein fluctuations used for inference; (iv) the moment-closure method used for likelihood approximation. We find that for sample sizes typical of flow cytometry experiments, parameter estimation by maximizing the likelihood is as accurate as using Bayesian methods but with a much reduced computational time. We also show that the choice of moment-closure method is the crucial factor determining the maximum achievable accuracy of moment-based inference methods. Common likelihood approximation methods based on the linear noise approximation or the zero cumulants closure perform poorly for feedback loops with large protein–DNA binding rates or large protein bursts; this is exacerbated for highly heterogeneous cell populations. By contrast, approximating the likelihood using the linear-mapping approximation or conditional derivative matching leads to highly accurate parameter estimates for a wide range of conditions.

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Section: Methodsmentioning

confidence: 99%

Accuracy of parameter estimation for auto-regulatory transcriptional feedback loops from noisy data

Cao

Grima

2019

J. R. Soc. Interface.

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“…Bootstrap filter can outperform EKF (Gordon et al, 1993). Generalized method of moments with empirical sample moments is performed in (Kügler, 2012;Lück and Wolf, 2016) whereas moment based methods for parameters inference and optimum experiment design are considered in (Ruess and Lygeros, 2015). Expectation propagation (EP) for approximate Bayesian inference is studied in (Cseke et al, 2016).…”

Section: Other Statistical Methodsmentioning

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%

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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“…From its original application in the modeling of capital asset pricing [5], its use has grown to make it one of the central methods of econometric analysis [11]. In spite of its broad applicability, its use in the natural sciences has been quite limited, although it has been applied recently to the analysis of simulated stochastic chemical reaction networks [12]. In the GMM, the population moments of a random variable, as calculated from a suitable model, are compared to the sample moments as calculated from the measured data.…”

Section: Introductionmentioning

confidence: 99%

Analyzing dwell times with the Generalized Method of Moments

Piatt

Price

2019

PLoS ONE

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The Generalized Method of Moments (GMM) is a statistical method for the analysis of samples from random processes. First developed for the analysis of econometric data, the method is here formulated to extract hidden kinetic parameters from measurements of single molecule dwell times. Our method is based on the analysis of cumulants of the measured dwell times. We develop a general form of an objective function whose minimization can return estimates of decay parameters for any number of intermediates directly from the data. We test the performance of our technique using both simulated and experimental data. We also compare the performance of our method to nonlinear least-squares minimization (NL-LSQM), a commonly-used technique for analysis of single molecule dwell times. Our findings indicate that the GMM performs comparably to NL-LSQM over most of the parameter range we explore. It offers some benefits compared with NL-LSQM in that it does not require binning, exhibits slightly lower bias and variance with small sample sizes (N<20), and is somewhat superior in identifying fast decay times with these same low count data sets. Additionally, a comparison with the Classical Method of Moments (CMM) shows that the CMM can fail in many cases, whereas the GMM always returns estimates. Our results show that the GMM can be a useful tool and complements standard approaches to analysis of single molecule dwell times.

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Generalized method of moments for estimating parameters of stochastic reaction networks

Cited by 29 publications

References 55 publications

Accuracy of parameter estimation for auto-regulatory transcriptional feedback loops from noisy data

Accuracy of parameter estimation for auto-regulatory transcriptional feedback loops from noisy data

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

Analyzing dwell times with the Generalized Method of Moments

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