Abstract
Parameter estimation is central for the analysis of models in Systems Biology. Stochastic models are of increasing importance. However, parameter estimation for stochastic models is still in the early phase of development and there is need for efficient methods to estimate model parameters from time course data which is intrinsically stochastic, only partially observed and has measurement noise. The thesis investigates methods for parameter estimation for stochastic models presenting one efficient method based on integration of ordinary differential equations (ODE) which allows parameter estimation even for models which have qualitatively different behavior in stochastic modeling compared to modeling with ODEs. Further methods proposed in the thesis are based on stochastic simulations. One of the methods uses the stochastic simulations for an estimation of the transition probabilities in the likelihood function. This method is suggested as an addition to the ODE-based method and should be used in systems with few reactions and small state spaces. The resulting stochastic optimization problem can be solved with a Particle Swarm algorithm. To this goal a stopping criterion suited to the stochasticity is proposed. Another approach is a transformation to a deterministic optimization problem. Therefore the polynomial chaos expansion is extended to stochastic functions in this thesis and then used for the transformation. The ODE-based method is motivated from a fast and efficient method for parameter estimation for systems of ODEs. A multiple shooting procedure is used in which the continuity constraints are omitted to allow for stochasticity. Unobserved states are treated by enlarging the optimization vector or using resulting values from the forward integration. To see how well the method covers the stochastic dynamics some test functions will be suggested. It is demonstrated that the method works well even in systems which have qualitatively different behavior in stochastic modeling than in modeling with ODEs. From a computational point of view, this method allows to tackle systems as large as those tackled in deterministic modeling.
Highlights
Parameter estimation is very important for the analysis of models in systems biology
The article presents a method for parameter estimation in stochastic models, based on short time Ordinary Differential Equations (ODE) integration
The method is able to estimate parameters, even in models which behave qualitatively different in stochastic modeling than in ODE modeling [27]
Summary
Parameter estimation is very important for the analysis of models in systems biology. We have identified a number of desirable properties that a parameter estimation procedure should have, in order to be useful in actual biological applications: It should work with measurements from few or even a single realization of the physical process, i.e. it should not require that enough measurements are made to reconstruct reliable probability distributions, or other statistical measures for all time points. It should work in cases where only partial measurements of the systems’ state are possible, obviously including measurement errors. This means that a wide range of numerical optimization techniques can be employed, including gradient based local methods, numerous global optimization schemes, or Bayesian approaches
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