Unbiased approximation of posteriors via coupled particle Markov chain Monte Carlo

Markov chain Monte Carlo (MCMC) is a powerful methodology for the approximation of posterior distributions. However, the iterative nature of MCMC does not naturally facilitate its use with modern highly parallelisable computation on HPC and cloud environments. Another concern is the identification of the bias and Monte Carlo error of produced averages. The above have prompted the recent development of fully (`embarrassingly') parallelisable unbiased Monte Carlo methodology based on couplings of MCMC algorithms. A caveat is that formulation of effective couplings is typically not trivial and requires model-specific technical effort. We propose couplings of sequential Monte Carlo (SMC) by considering adaptive SMC to approximate complex, high-dimensional posteriors combined with recent advances in unbiased estimation for state-space models. Coupling is then achieved at the SMC level and is, in general, not problem-specific. The resulting methodology enjoys desirable theoretical properties. We illustrate the effectiveness of the algorithm via application to two statistical models in high dimensions: (i) horseshoe regression; (ii) Gaussian graphical models