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Team:TU Munich/Modeling/Methods
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Another issue with this approach that it gives no information on the shape of the error function in the neighborhood of the obtained fit. Although it is possible to obtain information about the curvature by computing the hessian of the error function, but this can be very computationally intensive and only provides very local information. | Another issue with this approach that it gives no information on the shape of the error function in the neighborhood of the obtained fit. Although it is possible to obtain information about the curvature by computing the hessian of the error function, but this can be very computationally intensive and only provides very local information. | ||
| - | Hence another approach is | + | Hence another approach is desirable. |
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== Bayesian Inference == | == Bayesian Inference == | ||
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| + | == Monte Carlo Methods == | ||
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== Vision == | == Vision == | ||
Revision as of 18:28, 30 August 2012
Contents |
Modeling Methods
Responsible: Fabian Froehlich
Motivation
Why Mathematical Models
To be able to predict the behavior of a given biological system, one has to create a mathematical model of the system. The model is usually generated according to the Law of Mass Action[reference] and then simplified by assuming certain reactions to be fast. This model then could e.g. facilitate optimizations of bio-synthetic pathways by regulating the relative expression levels of the involved enzymes.
Why are we not necesserily interested in the best fit
To create a model that produces quantitative predictions, one needs to tune the parameters to fit experimental data. This procedure is called inference and is usually accomplished by computing the least squares[reference] approximation of the model to the experimental data with respect to the parameters.
There are several difficulties with this approach: In the case of a non-convex least squares error function several local minima may exist and optimizations algorithms will struggle to find all of them. This means one might not be able to find the best fit or even a biologically reasonable fit.
Another issue with this approach that it gives no information on the shape of the error function in the neighborhood of the obtained fit. Although it is possible to obtain information about the curvature by computing the hessian of the error function, but this can be very computationally intensive and only provides very local information.
Hence another approach is desirable.
Bayesian Inference
Monte Carlo Methods
