Imperial College London

DrBenCalderhead

Faculty of Natural SciencesDepartment of Mathematics

Lecturer in Statistics
 
 
 
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Contact

 

+44 (0)20 7594 8577b.calderhead

 
 
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Location

 

523Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Kramer:2014:10.1186/1471-2105-15-253,
author = {Kramer, A and Calderhead, B and Radde, N},
doi = {10.1186/1471-2105-15-253},
journal = {BMC BIOINFORMATICS},
title = {Hamiltonian Monte Carlo methods for efficient parameter estimation in steady state dynamical systems},
url = {http://dx.doi.org/10.1186/1471-2105-15-253},
volume = {15},
year = {2014}
}

RIS format (EndNote, RefMan)

TY  - JOUR
AB - BackgroundParameter 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.ResultsWe 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
AU - Kramer,A
AU - Calderhead,B
AU - Radde,N
DO - 10.1186/1471-2105-15-253
PY - 2014///
SN - 1471-2105
TI - Hamiltonian Monte Carlo methods for efficient parameter estimation in steady state dynamical systems
T2 - BMC BIOINFORMATICS
UR - http://dx.doi.org/10.1186/1471-2105-15-253
UR - http://hdl.handle.net/10044/1/64000
VL - 15
ER -