Speaker: Massimiliano Tamborrino
Abstract: Approximate Bayesian Computation (ABC) method has become one of the major tools for parameter inference in complex mathematical models in the last decade. The method is based on the idea of deriving an approximate posterior density aiming to target the true (unavailable) posterior by running massive simulations from the model to replace the intractable likelihood. When applying ABC to stochastic models, the derivation of effective summary statistics and proper distances is particularly challenging, since simulations from the model under the same parameter configuration result in different output. Moreover, since exact simulation from complex stochastic models is rarely possible, reliable (?) numerical methods need to be applied.
In this talk, I show how to use the underlying structural properties of the model to construct specific ABC summaries that are less sensitive to the intrinsic stochasticity of the model and the importance of adopting reliable property-preserving numerical (splitting) schemes for the synthetic data generation. Indeed, the commonly used Euler-Maruyama scheme drastically fails even with very small stepsizes. The approach is illustrated on the broad class of partially observed Hamiltonian stochastic differential equations, both with simulated and with real electroencephalography data.