We consider the problem of approximate Bayesian parameter inference in nonlinear state space models with intractable likelihoods. Sequential Monte Carlo with approximate Bayesian computations (SMC-ABC) is an 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 statistical simulation . We propose a  novel method based on the combination of Gaussian process optimisation (GPO) and SMC-ABC to create a Laplace approximation of the intractable posterior. The properties of the resulting GPO-ABC method are studied using stochastic volatility (SV) models with both synthetic and real-world data . We conclude that the algorithm enjoys: good accuracy comparable to particle Markov chain Monte Carlo with a significant reduction in computational cost and better robustness to noise in the estimates compared with a gradient-based optimisation algorithm. Finally, we make use of GPO-ABC to estimate the Value-at-Risk for a portfolio using a copula model with SV models for the margins .
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 .
R
nonlinear state space
non-linear state-space
R
an
one
R
statistical simulation
Monte Carlo methods
A
computationally efficient
D
(GPO)
R
The properties of the resulting GPO-ABC method are studied using stochastic volatility (SV)
We exemplify the proposed algorithm for inference in stochastic volatility
R
. We conclude that the algorithm enjoys: good accuracy comparable to particle Markov chain Monte Carlo with a significant reduction in computational cost and better robustness to noise in the estimates compared with a gradient-based optimisation algorithm. Finally, we make use of GPO-ABC to estimate the
as well as for estimating the
R
a portfolio
two portfolios
R
with SV models for the margins
. We document speed-ups of between one and two orders of magnitude compared to state-of-the-art algorithms for posterior inference