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Hamiltonian Monte Carlo methods for efficient parameter estimation in steady state dynamical systems.
BMC Bioinformatics. 2014 Jul 28; 15:253.BB

Abstract

BACKGROUND

Parameter estimation for differential equation models of intracellular processes is a highly relevant bu challenging task. The available experimental data do not usually contain enough information to identify all parameters uniquely, resulting in ill-posed estimation problems with often highly correlated parameters. Sampling-based Bayesian statistical approaches are appropriate for tackling this problem. The samples are typically generated via Markov chain Monte Carlo, however such methods are computationally expensive and their convergence may be slow, especially if there are strong correlations between parameters. Monte Carlo methods based on Euclidean or Riemannian Hamiltonian dynamics have been shown to outperform other samplers by making proposal moves that take the local sensitivities of the system's states into account and accepting these moves with high probability. However, the high computational cost involved with calculating the Hamiltonian trajectories prevents their widespread use for all but the smallest differential equation models. The further development of efficient sampling algorithms is therefore an important step towards improving the statistical analysis of predictive models of intracellular processes.

RESULTS

We show how state of the art Hamiltonian Monte Carlo methods may be significantly improved for steady state dynamical models. We present a novel approach for efficiently calculating the required geometric quantities by tracking steady states across the Hamiltonian trajectories using a Newton-Raphson method and employing local sensitivity information. Using our approach, we compare both Euclidean and Riemannian versions of Hamiltonian Monte Carlo on three models for intracellular processes with real data and demonstrate at least an order of magnitude improvement in the effective sampling speed. We further demonstrate the wider applicability of our approach to other gradient based MCMC methods, such as those based on Langevin diffusions.

CONCLUSION

Our approach is strictly benefitial in all test cases. The Matlab sources implementing our MCMC methodology is available from https://github.com/a-kramer/ode_rmhmc.

Authors+Show Affiliations

Institute for Systems Theory and Automatic Control, Pfaffenwaldring 9, 70550 Stuttgart, Germany. andrei.kramer@ist.uni-stuttgart.de.No affiliation info availableNo affiliation info available

Pub Type(s)

Journal Article

Language

eng

PubMed ID

25066046

Citation

Kramer, Andrei, et al. "Hamiltonian Monte Carlo Methods for Efficient Parameter Estimation in Steady State Dynamical Systems." BMC Bioinformatics, vol. 15, 2014, p. 253.
Kramer A, Calderhead B, Radde N. Hamiltonian Monte Carlo methods for efficient parameter estimation in steady state dynamical systems. BMC Bioinformatics. 2014;15:253.
Kramer, A., Calderhead, B., & Radde, N. (2014). Hamiltonian Monte Carlo methods for efficient parameter estimation in steady state dynamical systems. BMC Bioinformatics, 15, 253. https://doi.org/10.1186/1471-2105-15-253
Kramer A, Calderhead B, Radde N. Hamiltonian Monte Carlo Methods for Efficient Parameter Estimation in Steady State Dynamical Systems. BMC Bioinformatics. 2014 Jul 28;15:253. PubMed PMID: 25066046.
* Article titles in AMA citation format should be in sentence-case
TY - JOUR T1 - Hamiltonian Monte Carlo methods for efficient parameter estimation in steady state dynamical systems. AU - Kramer,Andrei, AU - Calderhead,Ben, AU - Radde,Nicole, Y1 - 2014/07/28/ PY - 2014/01/15/received PY - 2014/07/07/accepted PY - 2014/7/29/entrez PY - 2014/7/30/pubmed PY - 2014/11/9/medline SP - 253 EP - 253 JF - BMC bioinformatics JO - BMC Bioinformatics VL - 15 N2 - BACKGROUND: Parameter estimation for differential equation models of intracellular processes is a highly relevant bu challenging task. The available experimental data do not usually contain enough information to identify all parameters uniquely, resulting in ill-posed estimation problems with often highly correlated parameters. Sampling-based Bayesian statistical approaches are appropriate for tackling this problem. The samples are typically generated via Markov chain Monte Carlo, however such methods are computationally expensive and their convergence may be slow, especially if there are strong correlations between parameters. Monte Carlo methods based on Euclidean or Riemannian Hamiltonian dynamics have been shown to outperform other samplers by making proposal moves that take the local sensitivities of the system's states into account and accepting these moves with high probability. However, the high computational cost involved with calculating the Hamiltonian trajectories prevents their widespread use for all but the smallest differential equation models. The further development of efficient sampling algorithms is therefore an important step towards improving the statistical analysis of predictive models of intracellular processes. RESULTS: We show how state of the art Hamiltonian Monte Carlo methods may be significantly improved for steady state dynamical models. We present a novel approach for efficiently calculating the required geometric quantities by tracking steady states across the Hamiltonian trajectories using a Newton-Raphson method and employing local sensitivity information. Using our approach, we compare both Euclidean and Riemannian versions of Hamiltonian Monte Carlo on three models for intracellular processes with real data and demonstrate at least an order of magnitude improvement in the effective sampling speed. We further demonstrate the wider applicability of our approach to other gradient based MCMC methods, such as those based on Langevin diffusions. CONCLUSION: Our approach is strictly benefitial in all test cases. The Matlab sources implementing our MCMC methodology is available from https://github.com/a-kramer/ode_rmhmc. SN - 1471-2105 UR - https://www.unboundmedicine.com/medline/citation/25066046/Hamiltonian_Monte_Carlo_methods_for_efficient_parameter_estimation_in_steady_state_dynamical_systems_ L2 - https://bmcbioinformatics.biomedcentral.com/articles/10.1186/1471-2105-15-253 DB - PRIME DP - Unbound Medicine ER -