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

## TL;DR

This paper introduces perturbed MCMC algorithms that recycle past samples to accelerate approximate Bayesian methods like ABC and BSL, making complex Bayesian analyses more computationally feasible.

## Contribution

It presents a novel MCMC approach that enhances efficiency of ABC and BSL by leveraging sample recycling, supported by theoretical analysis and empirical validation.

## Key findings

- Significant reduction in the number of simulations needed.
- Maintains accuracy while improving computational speed.
- Effective in complex Bayesian models.

## Abstract

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 to have likelihood functions that elude analytical formulations. Even under such adversity, when one can simulate from the sampling distribution, Bayesian analysis can be conducted using approximate methods such as Approximate Bayesian Computation (ABC) or Bayesian Synthetic Likelihood (BSL). A significant drawback of these methods is that the number of required simulations can be prohibitively large, thus severely limiting their scope. In this paper we design perturbed MCMC samplers that can be used within the ABC and BSL paradigms to significantly accelerate computation while maintaining control on computational efficiency. The proposed strategy relies on recycling samples from the chain's past. The algorithmic design is supported by a theoretical analysis while practical performance is examined via a series of simulation examples and data analyses.