Structured Approximate Bayesian Inference for Models with Complex Likelihoods

Authors: Khaled Ouafi

We investigate the issue of approximate Bayesian parameter inference in nonlinear state space models with complex 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 expensive which hinders cost-effective implementations using standard methods based on optimisation and statistical simulation. We propose a innovational 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.

Comments: 9 Pages.

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Submission history

[v1] 2015-07-05 07:21:38

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