A Comparison of Methods for Guiding Adaptive Markov Chain Monte Carlo Algorithms in in Silico Model-Based Inference

Mathematical models are cognitive tools used to formalize our causal understanding of systems.  They are formulated by testing our knowledge about system behavior against available data through simulation; this process is known as in silico model-based inference.  In order to make statements of confidence about our knowledge, we must first remove the uncertainty due to our ignorance of the model parameters.  Mathematically, this is formulated as an integration of model predictions over all plausible combinations of parameter values.  This integration can be performed by an algorithm known as the Markov chain Monte Carlo, which takes a random walk in the parameter space, guided by local knowledge about the shape of the space.  Various approaches exist for guiding the random walk, but their efficacies and efficiencies have not yet been thoroughly investigated.  This study aimed to determine the relative efficacies and efficiencies of various adaptive forms of the algorithm in reference to the non-adaptive form.  We compared the success of Markov chain Monte Carlo algorithms performed with three different methods to propose new steps: one that adapted to the system based on an empirical estimate of the covariance of parameters, one that used a local metric of sensitivity to parameters, and one that ignored differences in parameter sensitivities as a control.  We also compared multiple adaptive algorithms with different frequencies of adaptation.  The algorithms were tested for their ability to extract known values for a simple, five-parameter model based on Michaelis Menten kinetics, from a synthetic data set that contained white noise.  We found that the adaptive algorithm similarly characterized the relations between the three principle parameters, as compared with the non-adaptive algorithm, even at a low number of iterations, and at a low frequency of adaptation.  The development of an accurate and computationally efficient algorithm is especially important for the analysis of higher dimensional systems, encountered in the modeling of cellular signaling processes, as well as economics, control engineering, and population modeling.