Finding our Way in the Dark: Approximate MCMC for Approximate Bayesian Methods

With larger data at their disposal, scientists are emboldened to tackle complex questions that require sophisticated statistical models. It is not unusual for the latter have likelihood functions elude analytical formulations. Even under such adversity, when one can simulate from sampling distribution, Bayesian analysis be conducted using approximate methods as Approximate Computation (ABC) or Synthetic Likelihood (BSL). A significant drawback of these number required simulations prohibitively large, thus severely limiting scope. In this paper we design perturbed MCMC samplers used within ABC and BSL paradigms significantly accelerate computation while maintaining control on computational efficiency. The proposed strategy relies recycling samples chain’s past. algorithmic supported by a theoretical practical performance examined via series simulation examples analyses.