Abstract
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 diffusions.ConclusionOur 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.Electronic supplementary materialThe online version of this article (doi:10.1186/1471-2105-15-253) contains supplementary material, which is available to authorized users.
Highlights
Parameter estimation for differential equation models of intracellular processes is a highly relevant bu challenging task
The major difficulty that arises generally for Hamiltonian Monte Carlo (HMC) type algorithms when dealing with ordinary differential equations (ODE) models is that the model outputs and their sensitivities have to be simulated at every point along trajectories in parameter space. We address this computational issue by proposing an extension to HMC algorithms especially designed to sample efficiently from models with steady state data under multiple perturbations
We evaluate our approach on three different steady state models with real data: a model for Erk phosphorylation in the MAPK signaling pathway, and two alternative models for the phosphorylation of insulin receptor substrate IRS after insulin stimulation
Summary
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, such methods are computationally expensive and their convergence may be slow, especially if there are strong correlations between parameters. The further development of efficient sampling algorithms is an important step towards improving the statistical analysis of predictive models of intracellular processes. Parameter estimation is a major task that paves the way for building predictive models of intracellular regulation processes. Variants of these core algorithms are widely available in parameter estimation software packages, e.g. GNU MCSIM [6], or the MCMCSTAT MATLAB toolbox [7]
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