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A Bayesian approach for parameter estimation in the extended clock gene circuit of Arabidopsis thaliana.

Higham CF, Husmeier D - BMC Bioinformatics (2013)

Bottom Line: The parameters have been fitted heuristically to available gene expression time series data and the calibrated model has been shown to reproduce the behaviour of the clock components.Ongoing work is extending the clock model to cover downstream effects, in particular metabolism, necessitating further parameter estimation and model selection.Using an efficient adaptive MCMC proposed by Haario et al. and working in a high performance computing setting, we quantify the posterior distribution around the proposed parameter values and explore the basin of attraction.

View Article: PubMed Central - HTML - PubMed

ABSTRACT
The circadian clock is an important molecular mechanism that enables many organisms to anticipate and adapt to environmental change. Pokhilko et al. recently built a deterministic ODE mathematical model of the plant circadian clock in order to understand the behaviour, mechanisms and properties of the system. The model comprises 30 molecular species (genes, mRNAs and proteins) and over 100 parameters. The parameters have been fitted heuristically to available gene expression time series data and the calibrated model has been shown to reproduce the behaviour of the clock components. Ongoing work is extending the clock model to cover downstream effects, in particular metabolism, necessitating further parameter estimation and model selection. This work investigates the challenges facing a full Bayesian treatment of parameter estimation. Using an efficient adaptive MCMC proposed by Haario et al. and working in a high performance computing setting, we quantify the posterior distribution around the proposed parameter values and explore the basin of attraction. We investigate if Bayesian inference is feasible in this high dimensional setting and thoroughly assess convergence and mixing with different statistical diagnostics, to prevent apparent convergence in some domains masking poor mixing in others.

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Posterior probability density estimates for parameters with low end PSRFs (left column) and parameters with high end PSRFs (right column). True parameter values are indicated by a cross on the x-axis.
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Figure 2: Posterior probability density estimates for parameters with low end PSRFs (left column) and parameters with high end PSRFs (right column). True parameter values are indicated by a cross on the x-axis.

Mentions: As mentioned above, convergence in data space at the species level decreases with distance, most notably as ED0 crosses EDm. Hence we checked whether convergence in parameter space was correlated to initial start values. We found that neither ED0 nor the percentage of ED0 to the true value is significantly correlated (P >0.05) with the PSRF for Experiments 1-7. Examination of the marginal posterior distributions for the five parameters with the lowest PSRFs and the five highest in Experiment 6 (Figure 2) illustrates that recovery of the true parameter values may not be controlled directly by convergence diagnostics.


A Bayesian approach for parameter estimation in the extended clock gene circuit of Arabidopsis thaliana.

Higham CF, Husmeier D - BMC Bioinformatics (2013)

Posterior probability density estimates for parameters with low end PSRFs (left column) and parameters with high end PSRFs (right column). True parameter values are indicated by a cross on the x-axis.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3750527&req=5

Figure 2: Posterior probability density estimates for parameters with low end PSRFs (left column) and parameters with high end PSRFs (right column). True parameter values are indicated by a cross on the x-axis.
Mentions: As mentioned above, convergence in data space at the species level decreases with distance, most notably as ED0 crosses EDm. Hence we checked whether convergence in parameter space was correlated to initial start values. We found that neither ED0 nor the percentage of ED0 to the true value is significantly correlated (P >0.05) with the PSRF for Experiments 1-7. Examination of the marginal posterior distributions for the five parameters with the lowest PSRFs and the five highest in Experiment 6 (Figure 2) illustrates that recovery of the true parameter values may not be controlled directly by convergence diagnostics.

Bottom Line: The parameters have been fitted heuristically to available gene expression time series data and the calibrated model has been shown to reproduce the behaviour of the clock components.Ongoing work is extending the clock model to cover downstream effects, in particular metabolism, necessitating further parameter estimation and model selection.Using an efficient adaptive MCMC proposed by Haario et al. and working in a high performance computing setting, we quantify the posterior distribution around the proposed parameter values and explore the basin of attraction.

View Article: PubMed Central - HTML - PubMed

ABSTRACT
The circadian clock is an important molecular mechanism that enables many organisms to anticipate and adapt to environmental change. Pokhilko et al. recently built a deterministic ODE mathematical model of the plant circadian clock in order to understand the behaviour, mechanisms and properties of the system. The model comprises 30 molecular species (genes, mRNAs and proteins) and over 100 parameters. The parameters have been fitted heuristically to available gene expression time series data and the calibrated model has been shown to reproduce the behaviour of the clock components. Ongoing work is extending the clock model to cover downstream effects, in particular metabolism, necessitating further parameter estimation and model selection. This work investigates the challenges facing a full Bayesian treatment of parameter estimation. Using an efficient adaptive MCMC proposed by Haario et al. and working in a high performance computing setting, we quantify the posterior distribution around the proposed parameter values and explore the basin of attraction. We investigate if Bayesian inference is feasible in this high dimensional setting and thoroughly assess convergence and mixing with different statistical diagnostics, to prevent apparent convergence in some domains masking poor mixing in others.

Show MeSH
Related in: MedlinePlus