  We consider the problem of approximate Bayesian parameter inference in
non-linear state-space models with intractable likelihoods. Sequential Monte
Carlo with approximate Bayesian computations (SMC-ABC) is one approach to
approximate the likelihood in this type of models. However, such approximations
can be noisy and computationally costly which hinders efficient implementations
using standard methods based on optimisation and Monte Carlo methods. We
propose a computationally efficient novel method based on the combination of
Gaussian process optimisation and SMC-ABC to create a Laplace approximation of
the intractable posterior. We exemplify the proposed algorithm for inference in
stochastic volatility models with both synthetic and real-world data as well as
for estimating the Value-at-Risk for two portfolios using a copula model. We
document speed-ups of between one and two orders of magnitude compared to
state-of-the-art algorithms for posterior inference.
