Hamiltonian Approximate Bayesian Computation

Likelihood-based methods have many appealing features, but they are difficult to use for models which do not have a closed-form, tractable likelihood function. When these models can be solved numerically and simulated, indirect inference can be used. In a Bayesian context, this approach is called Approximate Bayesian Computation (ABC). ABC methods using an extension of the Metropolis-Hastings algorithm (Marjoram et al 2003) allow sampling from the posterior using simulation, but are not effective for larger dimensions. Hamiltonian Monte Carlo (Neal 2012) and related algorithms can overcome these problems when the likelihood is available. Hamiltonian Approximate Bayesian Computation combines the ABC methodology with the Hamiltonian approach.