Hamiltonian Monte Carlo methods for efficient parameter estimation in steady state dynamical systems

BMC Bioinformatics

Andrei Kramer¹  Ben Calderhead²  Nicole Radde¹ 

[1] Institute for Systems Theory and Automatic Control, Pfaffenwaldring 9, 70550 Stuttgart, Germany

[2] Department of Mathematics, Imperial College London, London SW7 2AZ, UK

关键词: Systems biology;    Steady state data;    Hybrid monte carlo;    Parameter estimation;    MCMC methods;   

Others  :  1087539
DOI  :  10.1186/1471-2105-15-253

 received in 2014-01-15, accepted in 2014-07-07,  发布年份 2014

【 摘 要 】

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 webcite.

【 授权许可】

   
2014 Kramer et al.; licensee BioMed Central Ltd.

【 图 表 】

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