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More low-level communication mechanisms only allow for a quantitative analysis of the occurrence of message types, the frequency of message sequences, and the empirical distributions of parameter values.
In order to facilitate comparisons to help determine the significance of temporal information contained in parameter contours as opposed to the statistical distributions of parameter values, another classification system based on Gaussian mixture models (GMMs) was set up.
Since we still know little about the distributions of parameter values for real biological systems, we used uniform probability distribution for each parameter in this paper.
In addition, distributions of parameter values from MCMC samples were visualized using Tracer v.1.5 (available from http://tree.bio.ed.ac.uk/software/tracer/) to check mixing, choose a suitable burn-in, and look for trends that might suggest problems with convergence.
Actually, when the distributions of parameter values are compared, the values of betweenness, clustering coefficient and connectivity are significantly higher for the reference modules than for co-expression modules or signatures whereas the number of components is significantly lower, which clearly demonstrates the higher network structure of the former with respect to the later (Table 4).
MCMC samples from the two runs were combined after checking the distributions of parameter values using Tracer 1.5 (available from http://tree.bio.ed.ac.uk/software/tracer/).ac.uk/software/tracer/
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It is also expressed as the standard error of the mean by assuming normal distribution of parameter values.
Similar to RSA, DYNIA calculates the probability distribution of parameter values in behavioral parameter sets, but doing so for each individual model time step.
Since the linearization method is based on the assumption of normal distribution of parameter values, the Monte Carlo and bootstrap methods may be preferred to the linearization method.
Nonlinear regression programs usually give the parameter uncertainty by calculating the standard error of the mean, and assuming linear relationship between variables in the vicinity of the estimated parameter values and normal distribution of parameter values.
To achieve this result we employed the Covariance Matrix Adaptation Evolution Strategy (CMA-ES), an iterative process in which samples are created based on a distribution of parameter values that evolve over time to better fit an objective function.
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