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.
Highlights
Since the early 1990s Bayesian statisticians have been able to operate largely due to the rapid development of Markov chain Monte Carlo (MCMC) sampling methods
In the two sections we extend the work of Johndrow et al (2015b) on the perturbed MCMC and in Section 6.3 discuss necessary conditions for the ergodicity of AABC and Approximated BSL (ABSL)
In this paper we propose to speed up generic Approximate Bayesian Computation (ABC)-MCMC and Bayesian Synthetic Likelihood (BSL) algorithms by reusing past simulations
Summary
Since the early 1990s Bayesian statisticians have been able to operate largely due to the rapid development of Markov chain Monte Carlo (MCMC) sampling methods (see, for example Craiu and Rosenthal, 2014, for a recent review). In the absence of a tractable likelihood function, statisticians have developed approximate methods to perform Bayesian inference when, for any parameter value θ ∈ Rq, data y ∼ f (y|θ) can be sampled from the model. We consider two alternative approaches that have been proposed and gained considerable momentum in recent years: the Approximate Bayesian Computation (ABC) (Marin et al, 2012; Baragatti and Pudlo, 2014; Sisson et al, 2018a; Drovandi, 2018) and the Bayesian Synthetic Likelihood (BSL) (Wood, 2010; Drovandi et al, 2018a; Price et al, 2018) Both algorithms are effective when they are combined with Markov chain Monte Carlo sampling schemes to produce samples from an approximation of π and both share the need for generating many pseudo-data sets y ∼ f (y|θ). The paper closes with ideas for future work and conclusions
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