  In modern days, the ability to carry out computations in parallel is key to
efficient implementations of computationally intensive algorithms. This paper
investigates the applicability of the previously proposed Augmented Island
Resampling Particle Filter (AIRPF) -- an algorithm designed for parallel
implementations -- to particle Markov Chain Monte Carlo (PMCMC). We show that
AIRPF produces a non-negative unbiased estimator of the marginal likelihood and
hence is suitable for PMCMC. We also prove stability properties, similar to
those of the $\alpha$SMC algorithm, for AIRPF. This implies that the error of
AIRPF can be bounded uniformly in time by controlling the effective number of
filters, which in turn can be done by adaptively constraining the interactions
between filters. We demonstrate the superiority of AIRPF over independent
Bootstrap Particle Filters, not only numerically, but also theoretically. To
this end, we extend the previously proposed collision analysis approach to
derive an explicit expression for the variance of the marginal likelihood
estimate. This expression admits exact evaluation of the variance in some
simple scenarios as we shall also demonstrate.
