The development of chemical reaction models aids system design and optimization, along with fundamental understanding, in a number of areas such as combustion, catalysis, and biology. A systematic approach to building reaction network models uses available data not only to estimate unknown parameters, but to also learn the *model structure*. Bayesian inference provides a natural approach for this data-driven construction of models. The traditional Bayesian model inference methodology is based on evaluating a multidimensional integral for each model. This is often not feasible for reaction network inference, as the number of plausible models can be very large. An alternative approach based on model-space sampling can enable large-scale network inference, but its efficient implementation continues to be a challenge.

In this talk, we present some newly developed computational methods that make large-scale nonlinear network inference tractable. Firstly, we exploit the network-based interactions of species to design improved between-model proposals for Markov chain Monte Carlo (MCMC). We then introduce a sensitivity-based determination of move types which, when combined with the above network-aware proposals, yields further sampling efficiency. We also show that by recognizing network inference as a fixed-dimensional problem with point-mass priors, we can adapt existing adaptive MCMC methods for network inference. Finally, we present an approximation-based method that allows sampling over very large model spaces whose exploration could be prohibitively expensive with exact sampling methods.