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Bayesian model comparison and parameter inference in systems biology using nested sampling.

Pullen N, Morris RJ - PLoS ONE (2014)

Bottom Line: We demonstrate how nested sampling can be used to reverse-engineer a system's behaviour whilst accounting for the uncertainty in the results.We show how the evidence and the model ranking can change as a function of the available data.Furthermore, the addition of data from extra variables of the system can deliver more information for model comparison than increasing the data from one variable, thus providing a basis for experimental design.

View Article: PubMed Central - PubMed

Affiliation: Computational and Systems Biology, John Innes Centre, Norwich, United Kingdom.

ABSTRACT
Inferring parameters for models of biological processes is a current challenge in systems biology, as is the related problem of comparing competing models that explain the data. In this work we apply Skilling's nested sampling to address both of these problems. Nested sampling is a Bayesian method for exploring parameter space that transforms a multi-dimensional integral to a 1D integration over likelihood space. This approach focuses on the computation of the marginal likelihood or evidence. The ratio of evidences of different models leads to the Bayes factor, which can be used for model comparison. We demonstrate how nested sampling can be used to reverse-engineer a system's behaviour whilst accounting for the uncertainty in the results. The effect of missing initial conditions of the variables as well as unknown parameters is investigated. We show how the evidence and the model ranking can change as a function of the available data. Furthermore, the addition of data from extra variables of the system can deliver more information for model comparison than increasing the data from one variable, thus providing a basis for experimental design.

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Related in: MedlinePlus

The inferred dynamics of the repressilator.Given just 26 noisy data points of cI protein (vermillion diamonds, bottom left) we were able to capture the full dynamics of the repressilator system with high accuracy, even when the mean estimates for the initial conditions of the other variables were not reflective of their true values. True solution, dashed black line; estimated dynamics using mean parameters, solid coloured lines; mean , filled ribbons.
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pone-0088419-g003: The inferred dynamics of the repressilator.Given just 26 noisy data points of cI protein (vermillion diamonds, bottom left) we were able to capture the full dynamics of the repressilator system with high accuracy, even when the mean estimates for the initial conditions of the other variables were not reflective of their true values. True solution, dashed black line; estimated dynamics using mean parameters, solid coloured lines; mean , filled ribbons.

Mentions: Using nested sampling we can produce an estimate of the means and standard deviations of the inferred parameters as explained in the Methods section. The actual values and inferred values are shown in Table 2. The system with these mean values as the actual parameters is shown in Figure 3 along with a ribbon representing . As can be seen, despite not estimating the initial conditions well, they are not that important for capturing the qualitative dynamics of the entire system. This is because the repressilator has a limit cycle and is therefore insensitive to most initial conditions. After the first peak the inferred oscillations match very closely to the true solution for all variables even though the algorithm only had a few, noisy data points available for one variable. The log-evidence for this model and data is .


Bayesian model comparison and parameter inference in systems biology using nested sampling.

Pullen N, Morris RJ - PLoS ONE (2014)

The inferred dynamics of the repressilator.Given just 26 noisy data points of cI protein (vermillion diamonds, bottom left) we were able to capture the full dynamics of the repressilator system with high accuracy, even when the mean estimates for the initial conditions of the other variables were not reflective of their true values. True solution, dashed black line; estimated dynamics using mean parameters, solid coloured lines; mean , filled ribbons.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3921180&req=5

pone-0088419-g003: The inferred dynamics of the repressilator.Given just 26 noisy data points of cI protein (vermillion diamonds, bottom left) we were able to capture the full dynamics of the repressilator system with high accuracy, even when the mean estimates for the initial conditions of the other variables were not reflective of their true values. True solution, dashed black line; estimated dynamics using mean parameters, solid coloured lines; mean , filled ribbons.
Mentions: Using nested sampling we can produce an estimate of the means and standard deviations of the inferred parameters as explained in the Methods section. The actual values and inferred values are shown in Table 2. The system with these mean values as the actual parameters is shown in Figure 3 along with a ribbon representing . As can be seen, despite not estimating the initial conditions well, they are not that important for capturing the qualitative dynamics of the entire system. This is because the repressilator has a limit cycle and is therefore insensitive to most initial conditions. After the first peak the inferred oscillations match very closely to the true solution for all variables even though the algorithm only had a few, noisy data points available for one variable. The log-evidence for this model and data is .

Bottom Line: We demonstrate how nested sampling can be used to reverse-engineer a system's behaviour whilst accounting for the uncertainty in the results.We show how the evidence and the model ranking can change as a function of the available data.Furthermore, the addition of data from extra variables of the system can deliver more information for model comparison than increasing the data from one variable, thus providing a basis for experimental design.

View Article: PubMed Central - PubMed

Affiliation: Computational and Systems Biology, John Innes Centre, Norwich, United Kingdom.

ABSTRACT
Inferring parameters for models of biological processes is a current challenge in systems biology, as is the related problem of comparing competing models that explain the data. In this work we apply Skilling's nested sampling to address both of these problems. Nested sampling is a Bayesian method for exploring parameter space that transforms a multi-dimensional integral to a 1D integration over likelihood space. This approach focuses on the computation of the marginal likelihood or evidence. The ratio of evidences of different models leads to the Bayes factor, which can be used for model comparison. We demonstrate how nested sampling can be used to reverse-engineer a system's behaviour whilst accounting for the uncertainty in the results. The effect of missing initial conditions of the variables as well as unknown parameters is investigated. We show how the evidence and the model ranking can change as a function of the available data. Furthermore, the addition of data from extra variables of the system can deliver more information for model comparison than increasing the data from one variable, thus providing a basis for experimental design.

Show MeSH
Related in: MedlinePlus