Bayesian model inference and parameter estimation for biological models

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The procedure returns joint probability distributions for model parameters and makes it possible to compute uncertainty for model-based predictions based on error in the data and the non-identifiability of model parameters. Bayesian methods also make it possible to compute the odds ratio for competing models having different numbers of parameters. Bayesian approaches to model calibration and discrimination represent a generally useful and rigorous approach to analyzing biochemical pathways in the face of parametric and topological uncertainty.

BayesSB uses a multi-start Markov Chain Monte Carlo (MCMC) search procedure to search the landscape of the objective function. To improve the efficiency of the search and improve chain convergence it is often necessary to perform adaptive MCMC walks. A drawback of some adaptive MCMC approaches is that they alter the proposal distribution (which determines how the next step is taken) over the course of a walk and this has the potential to violate stationarity, a necessary condition for correct sampling of posterior distributions. This issue should be evaluated when BayesSB is used.

BayesSB returns parameter estimates as array of size $C\times M\times (N+1)$ where $C$ is the number of MCMC chains, $M$ the number of steps, and $N$ the number of parameters ($N+1$ appears because we record a posterior value for each N-dimensional vector). Parameter distributions in this array co-vary in a strong and non-linear way and it is essential to use this covariation when analyzing parameters or making model-based predictions (reporting parameters as a table of values and associated variances is invalid). This is not a peculiarity of our approach but a fundamental property of mass-action models calibrated to time-course data.