I propose a Bayesian parameter estimation framework to facilitate model calibration and uncertainty analysis for predictive models of biological systems. Many of these models are nonlinear differential equations that characterize the dynamics of the relevant biochemical species. System biologists need to estimate many free parameters from sparse and noisy experimental data to calibrate these models. Despite the uncertainties associated with this data, systems biologists directly fit the free parameters, typically ignoring any uncertainty altogether. My work moves past this traditional model-fitting paradigm by adapting an approximate marginal Markov chain Monte Carlo (MCMC) method for Bayesian parameter estimation. I find that this method can recover the posterior parameter distribution from experimental data for a well-known biological system, the mitogen-activated protein kinase (MAPK) signaling pathway. This work introduces a new modeling paradigm that bridges the gap between standard systems biology modeling practices and rigorous uncertainty quantification.

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