Before revision:  We here show for an analytically solvable network model that the effective action in statistical field theory is identical to the rate function in large deviation theory; using field theoretical methods we derive this rate function . It takes the form of a Kullback-Leibler divergence and enables data-driven inference of model parameters and Bayesian prediction of time series  .
After revision:  We here show for an analytically solvable network model that the effective action in statistical field theory is identical to the rate function and derive the latter using field theory. This rate function takes the form of a Kullback-Leibler divergence and enables data-driven inference of model parameters and Bayesian prediction of time series .