Stochastic methods for parameter estimation and design of experiments in systems biology

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Markov Chain Monte Carlo (MCMC) methods are sampling techniques that utilize random numbers to approximate unknown deterministic values. These methods can estimate expected values, model parameters, and explore properties of complex, high-dimensional probability distributions. Bayesian analysis underpins parameter estimation through probabilistic sampling, highlighting the robustness and simplicity of these stochastic methods, even for nonlinear problems with multiple parameters and integrated uncertainty analysis. The Bayesian approach incorporates prior knowledge, enabling straightforward regularization of unidentifiable parameters. This work emphasizes typical scenarios in systems biology, including relative data, nonlinear ordinary differential equation models, and limited data points. It also examines the implications of parameter estimation from steady-state data, particularly performance improvements. In biological contexts, data is predominantly relative; raw measurements, such as western blot intensities, are normalized against control experiments or reference values, necessitating that models align their outputs accordingly. The study compares various sampling algorithms based on effective sampling speed and discusses necessary adaptations for handling relative and steady-state data.