Approximate maximum likelihood estimation using data-cloning ABC

We consider approximate maximum likelihood inference for a general class of models, using an approximate Bayesian computation (ABC) approach. The typical target of ABC methods are models with intractable likelihoods, and we merge an ABC-MCMC sampler with so-called "data cloning" for maximum likelihood estimation. The methodology should partly compensate for the inability to reduce the ABC-threshold to very small values. In our examples the threshold is set to fairly large (manageable) values, while the number of data-clones is increased to ease convergence of the Markov chain towards the (unattainable) maximum likelihood estimate. Simulation studies show the good performance of our approach on linear regression models and more challenging scenarios considering stochastic differential equations, also including state-space models.