trajectories do not exploit direct knowledge of the data. This sometimes result in many rejected proposals if the sample size is large. Carefully tuned Sequential Monte Carlo (SMC) strategies can be constructed so that the best trajectories (“particles”) are selected according to their proximity to data, and this have pushed forward Bayesian inference via MCMC methods incorporating SMC [@andrieu2010particle].

However for complex (ideally multidimensional) stochastic models and a large number of observations, use of SMC methods is computer intensive. Approximate Bayesian computation (ABC, see reviews by [@sisson-fan(2011)] and [@marin-et-al(2011)]) eases sampling from an approximation of the posterior distribution, by substituting likelihood function evaluations with simulations from the data generating model. Here follows a short discussion on ABC which will ease the introduction to our original contribution.

Basics of ABC {#sec:abc-basics}
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Here we summarize some minimal notions of ABC methodology, without considering for the moment the data-cloning scenario, hence in this section it can be assumed that $K=1$. The ABC approach considers generating samples $z$ from $f(\cdot)$ in (i.e. $z\in \mathsf{Y}$, same as the actual data) and corresponding proposals $\theta^{\#}$ are accepted if the $z$ are “close” to data $y$, according to a threshold $\delta>0$. Several criterion for “closeness” can 