Estimating Bayes factors via thermodynamic integration and population MCMC

Calderhead, Ben; Girolami, Mark

doi:10.1016/j.csda.2009.07.025

Cited by 150 publications

(185 citation statements)

References 19 publications

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“…0. To this end we combine our gradient matching with Gaussian processes with the tempering approach in [3] (for details on tempering: [17], [18]) and temper this parameter to zero. Consider a series of "temperatures", 0 = 1 < ... < M = 1 and a power posterior distribution of our ODE parameters [14] …”

Section: Methodsmentioning

confidence: 99%

Computational Inference in Systems Biology

Macdonald

Husmeier

2015

Lecture Notes in Computer Science

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Abstract. Parameter inference in mathematical models of biological pathways, expressed as coupled ordinary di↵erential equations (ODEs), is a challenging problem. The computational costs associated with repeatedly solving the ODEs are often high. Aimed at reducing this cost, new concepts using gradient matching have been proposed. This paper combines current adaptive gradient matching approaches, using Gaussian processes, with a parallel tempering scheme, and conducts a comparative evaluation with current methods used for parameter inference in ODEs.

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Section: Methodsmentioning

confidence: 99%

Computational Inference in Systems Biology

Macdonald

Husmeier

2015

Lecture Notes in Computer Science

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“…In this work, we embed these sampling schemes within a population MCMC framework to help escape local maxima and fully explore the parameter space [21,42,43].…”

Section: Differential Geometric Sampling Methods B Calderhead and Mmentioning

confidence: 99%

“…Initial proof of concept investigations has shown that a Bayesian approach to model ranking can be very successful [4,11]; however, it is acknowledged that performing Bayesian inference over ODE models is extremely challenging [21]. The procedure is equivalent to evaluating integrals involving a highly nonlinear function over a high-dimensional space.…”

Section: Introductionmentioning

confidence: 99%

Statistical analysis of nonlinear dynamical systems using differential geometric sampling methods

Calderhead

Girolami

2011

Interface Focus.

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Mechanistic models based on systems of nonlinear differential equations can help provide a quantitative understanding of complex physical or biological phenomena. The use of such models to describe nonlinear interactions in molecular biology has a long history; however, it is only recently that advances in computing have allowed these models to be set within a statistical framework, further increasing their usefulness and binding modelling and experimental approaches more tightly together. A probabilistic approach to modelling allows us to quantify uncertainty in both the model parameters and the model predictions, as well as in the model hypotheses themselves. In this paper, the Bayesian approach to statistical inference is adopted and we examine the significant challenges that arise when performing inference over nonlinear ordinary differential equation models describing cell signalling pathways and enzymatic circadian control; in particular, we address the difficulties arising owing to strong nonlinear correlation structures, high dimensionality and non-identifiability of parameters. We demonstrate how recently introduced differential geometric Markov chain Monte Carlo methodology alleviates many of these issues by making proposals based on local sensitivity information, which ultimately allows us to perform effective statistical analysis. Along the way, we highlight the deep link between the sensitivity analysis of such dynamic system models and the underlying Riemannian geometry of the induced posterior probability distributions.

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“…, n of the trajectory X * , made at time t i . Estimation can be done by classical estimators such as Nonlinear Least Squares (NLS), Maximum Likelihood Estimator (MLE) [27] or Bayesian approaches ( [21], [14], [6] and [15] for example). Nevertheless, the statistical estimation of an ODE model by NLS leads to a difficult nonlinear estimation problem.…”

Section: Such a Model Is Called An Initial Value Problem (Ivp) The Smentioning

confidence: 99%

A tracking approach to parameter estimation in linear ordinary differential equations

Brunel

Clairon

2015

Electron. J. Statist.

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Ordinary Differential Equations are widespread tools to model chemical, physical, biological process but they usually rely on parameters which are of critical importance in terms of dynamic and need to be estimated directly from the data. Classical statistical approaches (nonlinear least squares, maximum likelihood estimator) can give unsatisfactory results because of computational difficulties and ill-posedness of the statistical problem. New estimation methods that use some nonparametric devices have been proposed to circumvent these issues. We present a new estimator that shares properties with Two-Step estimator and Generalized Smoothing (introduced by Ramsay et al. [34]). We introduce a perturbed model and we use optimal control theory for constructing a criterion that aims at minimizing the discrepancy with data and the model. Here, we focus on the case of linear Ordinary Differential Equations as our criterion has a closed-form expression that permits a detailed analysis. Our approach avoids the use of a nonparametric estimator of the derivative, which is one of the main cause of inaccuracy in Two-Step estimators. Moreover, we take into account model discrepancy and our estimator is more robust to model misspecification than classical methods. The discrepancy with the parametric ODE model correspond to the minimum perturbation (or control) to apply to the initial model. Its qualitative analysis can be informative for misspecification diagnosis. In the case of well-specified model, we show the consistency of our estimator and that we reach the parametric √ n− rate when regression splines are used in the first step.

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Estimating Bayes factors via thermodynamic integration and population MCMC

Cited by 150 publications

References 19 publications

Computational Inference in Systems Biology

Computational Inference in Systems Biology

Statistical analysis of nonlinear dynamical systems using differential geometric sampling methods

A tracking approach to parameter estimation in linear ordinary differential equations

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