PMC:2654804 / 6581-8298 JSONTXT

{"target":"https://pubannotation.org/docs/sourcedb/PMC/sourceid/2654804","sourcedb":"PMC","sourceid":"2654804","source_url":"https://www.ncbi.nlm.nih.gov/pmc/2654804","text":"In particular, it is not sufficient to give only data from one or several experiments, or a source model from which such data can be simulated, see Figure 1A. In addition to the data, a model space must be defined, to specify the possible forms of the right-hand side of the ODEs and appropriate parameter ranges. Clearly, if we allow few possible reactions and narrow parameter ranges we obtain a simpler identification problem, and if we allow many possible reactions and wide parameter ranges we obtain a more difficult problem. Furthermore, known prior information about parts of the model may be given. Finally, we must define an objective function that also includes some notion of model complexity. This is needed since we are searching among different structures, and a simple maximum likelihood criterion is not sufficient and will lead to over-fitting. Together, this defines the identification problem mathematically as an optimization problem, the solution of which is a model. An illustration of an identification problem is shown in Figure 1B, and the solution model is shown in Figure 1C.\nFig. 1. Identification of ODE systems. (A) An identification problem can be specified with real or simulated data from one or several experiments, a model space of allowed reactions occurring on the right-hand side of the ODEs, an initial model representing prior knowledge and an error function. (B) An example of an identification problem with a model space of three traditional chemical reaction types, an error function where L=likelihood function, λ K=structural complexity term (λ=constant and K=number of model parameters) and an initial model with no prior information. (C) An example of a solution model.","divisions":[{"label":"label","span":{"begin":1104,"end":1111}}],"tracks":[]}