A Vine-copula Based Adaptive MCMC Sampler for Efficient Inference of Dynamical Systems

Schmidl, Daniel; Czado, Claudia; Hug, Sabine; Theis, Fabian J.

doi:10.1214/13-ba801

Cited by 19 publications

(22 citation statements)

References 34 publications

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“…The model, investigation, and temperature specific underlying Markov chain Monte Carlo (MCMC) samples were drawn using the recently introduced copula-based Metropolis-Hastings (MH) algorithm [23]. Copulas are constructs from probability theory for assessing and sampling from multivariate distributions.…”

Section: Methodsmentioning

confidence: 99%

“…However, due to very complex probability surfaces these approaches often struggle with sampling efficiency [22]. In order to avoid resulting convergence issues of the MCMC approach, we combined a technique called thermodynamic integration with a novel copula-based Metropolis-Hastings sampler [23]. This provides numerically stable results for the inference process.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian model selection validates a biokinetic model for zirconium processing in humans

Schmidl

Hug

et al. 2012

BMC Syst Biol

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BackgroundIn radiation protection, biokinetic models for zirconium processing are of crucial importance in dose estimation and further risk analysis for humans exposed to this radioactive substance. They provide limiting values of detrimental effects and build the basis for applications in internal dosimetry, the prediction for radioactive zirconium retention in various organs as well as retrospective dosimetry. Multi-compartmental models are the tool of choice for simulating the processing of zirconium. Although easily interpretable, determining the exact compartment structure and interaction mechanisms is generally daunting. In the context of observing the dynamics of multiple compartments, Bayesian methods provide efficient tools for model inference and selection.ResultsWe are the first to apply a Markov chain Monte Carlo approach to compute Bayes factors for the evaluation of two competing models for zirconium processing in the human body after ingestion. Based on in vivo measurements of human plasma and urine levels we were able to show that a recently published model is superior to the standard model of the International Commission on Radiological Protection. The Bayes factors were estimated by means of the numerically stable thermodynamic integration in combination with a recently developed copula-based Metropolis-Hastings sampler.ConclusionsIn contrast to the standard model the novel model predicts lower accretion of zirconium in bones. This results in lower levels of noxious doses for exposed individuals. Moreover, the Bayesian approach allows for retrospective dose assessment, including credible intervals for the initially ingested zirconium, in a significantly more reliable fashion than previously possible. All methods presented here are readily applicable to many modeling tasks in systems biology.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bayesian model selection validates a biokinetic model for zirconium processing in humans

Schmidl

Hug

et al. 2012

BMC Syst Biol

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“…Markov chain methods enjoy great popularity as method of choice for numerical computation of high-dimensional integrals. Despite numerous improvements [2,3] of the original methods, the number of function evaluations required to obtain a converged Markov chain for multi-modal and heavy-tailed posterior distributions is often large [5].…”

Section: Construction Of Approximation Nodesmentioning

confidence: 99%

“…For high-dimensional integration, Markov chain Monte Carlo (MCMC) generally is the method of choice [1]. There have been many developments for efficient computation of marginals using MCMC [2,3]. For example, the MCMC method can be combined with the Variational Bayes approach, which assumes that the posterior factorises over a partition of latent variables [4].…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, the derivation of the factorisation of the posterior can be intractable for many densities. Both of these issues frequently arise when estimating parameters in dynamical systems [3]. The evaluation of the likelihood, and thus also of the posterior, requires the solution of the dynamical system which often is not available in analytical form.…”

Section: Introductionmentioning

confidence: 99%

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Radial Basis Function Approximations of Bayesian Parameter Posterior Densities for Uncertainty Analysis

Fröhlich

Hroß

Theis

et al. 2014

Lecture Notes in Computer Science

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Abstract. Dynamical models are widely used in systems biology to describe biological processes ranging from single cell transcription of genes to the tissue scale formation of gradients for cell guidance. One of the key issues for this class of models is the estimation of kinetic parameters from given measurement data, the so called parameter estimation. Measurement noise and the limited amount of data, give rise to uncertainty in estimates which can be captured in a probability density over the parameter space. Unfortunately, studying this probability density, using e.g. Markov chain Monte-Carlo, is often computationally demanding as it requires the repeated simulation of the underlying model. In the case of highly complex models, such as PDE models, this can render the study intractable. In this paper, we will present novel methods for analysis of such probability densities using networks of radial basis functions. We employed lattice generation algorithms, adaptive interacting particle sampling schemes as well as classical sampling schemes for the generation of approximation nodes coupled to the respective weighting scheme and compared their efficiency on different application examples. Our analysis showed that the novel method can yield an expected L2 approximation error in marginals that is several orders of magnitude lower compared to classical approximations. This allows for a drastic reduction of the number of model evaluations. This facilitates the analysis of uncertainty for problems with high computational complexity. Finally, we successfully applied our method to a complex partial differential equation model for guided cell migration of dendritic cells.

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Uncertainty Analysis for Non-identifiable Dynamical Systems: Profile Likelihoods, Bootstrapping and More

Fröhlich

Theis

Hasenauer

2014

Lecture Notes in Computer Science

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A Vine-copula Based Adaptive MCMC Sampler for Efficient Inference of Dynamical Systems

Cited by 19 publications

References 34 publications

Bayesian model selection validates a biokinetic model for zirconium processing in humans

Bayesian model selection validates a biokinetic model for zirconium processing in humans

Radial Basis Function Approximations of Bayesian Parameter Posterior Densities for Uncertainty Analysis

Uncertainty Analysis for Non-identifiable Dynamical Systems: Profile Likelihoods, Bootstrapping and More

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