Uncertainty in Biology by Liesbet Geris & David Gomez-Cabrero

Author:Liesbet Geris & David Gomez-Cabrero
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

9.7 Discussion

The construction and selection of a mathematical model as a compact and predictive representation of a biochemical system is an active area of research that is likely only in its infancy for biochemical applications. Actually, when browsing the literature there are surprisingly few examples of comparisons between dynamical models of biochemical systems. In the analysis of many biochemical systems a single candidate model is assessed, which was already argued against by Chamberlain in 1890 [10]. As pointed out by Chamberlain, the construction of several models typically requires the researcher to think hard about alternative plausible explanations for the studied phenomena. However, recently a number of approaches has become available for the automatic construction of candidate models [20, 33, 52].

The most suitable method to assess a set of models depends on the structure of, and relation between, the candidate models as well as the experimental data. The likelihood ratio test is convenient for model discrimination, but it requires the candidate models to be nested, which is commonly not the case. Other criteria such as the AIC and BIC are also easy to handle, since only the optimal parameter point is required, but they are only asymptotically valid for large data sets. For small data sets, the researcher is left with the corrected AIC (and DIC) among the information theoretic approaches, and with the direct computation of posterior probabilities from Bayes factors. In the computation of posterior probabilities the researcher will commonly face issues such as the choice of the prior parameter distribution and the curse-of-dimensionality in the integration over high-dimensional parameter spaces. However, there are no available methods to avoid these issues, with a few exceptions (e.g., the BIC does not require prior distributions to be defined). Advanced computational methods for the integration of high-dimensional parameter spaces have been proposed [22], but it remains to be demonstrated that they are applicable for biochemical models.

We also note that (ad hoc) model selection criteria that do not fall under any of the main categories are sometimes useful. For example, a by now classical model for segmentation gene expression patterns in Drosophila was inferred by von Dassow et al. [58] using a goodness-of-fit function for pattern matching with the goal to resemble the judgment of an expert researcher. Lillacci et al. [36] used an extended Kalman filter to estimate statistical moments of states and parameters simultaneously, and used the overlap between model predictions and data as well as a test as criteria for model selection.

To accurately apply model selection methods it is important to understand the concepts underlying the alternative methods, and to be able to judge when a certain method is applicable and suitable. It is also important to understand the inherent issues and limitations of the available methods. With this chapter we hope to provide the reader with an overview of the current situation in this domain as well as an easily accessible resource for the purpose of model selection in biochemical applications. However, many of the discussed principles apply equally well in other domains of science and engineering.

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