  Almost all fields of science rely upon statistical inference to estimate
unknown parameters in theoretical and computational models. While the
performance of modern computer hardware continues to grow, the computational
requirements for the simulation of models are growing even faster. This is
largely due to the increase in model complexity, often including stochastic
dynamics, that is necessary to describe and characterize phenomena observed
using modern, high resolution, experimental techniques. Such models are rarely
analytically tractable, meaning that extremely large numbers of stochastic
simulations are required for parameter inference. In such cases, parameter
inference can be practically impossible. In this work, we present new
computational Bayesian techniques that accelerate inference for expensive
stochastic models by using computationally inexpensive approximations to inform
feasible regions in parameter space, and through learning transforms that
adjust the biased approximate inferences to closer represent the correct
inferences under the expensive stochastic model. Using topical examples from
ecology and cell biology, we demonstrate a speed improvement of an order of
magnitude without any loss in accuracy. This represents a substantial
improvement over current state-of-the-art methods for Bayesian computations
when appropriate model approximations are available.
