Title: Exploiting network topology for large-scale inference of nonlinear reaction models,
Abstract: The development of chemical reaction models aids understanding and prediction
in areas ranging from biology to electrochemistry and combustion. A systematic
approach to building reaction network models uses observational data not only
to estimate unknown parameters, but also to learn model structure. Bayesian
inference provides a natural approach to this data-driven construction of
models. Yet traditional Bayesian model inference methodologies that numerically
evaluate the evidence for each model are often infeasible for nonlinear
reaction network inference, as the number of plausible models can be
combinatorially large. Alternative approaches based on model-space sampling can
enable large-scale network inference, but their realization presents many
challenges. In this paper, we present new computational methods that make
large-scale nonlinear network inference tractable. First, we exploit the
topology of networks describing potential interactions among chemical species
to design improved "between-model" proposals for reversible-jump Markov chain
Monte Carlo. Second, we introduce a sensitivity-based determination of move
types which, when combined with network-aware proposals, yields significant
additional gains in sampling performance. These algorithms are demonstrated on
inference problems drawn from systems biology, with nonlinear differential
equation models of species interactions.