Stratified Distance Space Improves the Efficiency of Sequential Samplers for Approximate Bayesian Computation

Approximate Bayesian computation (ABC) methods are standard tools for inferring parameters of complex models when the likelihood function is analytically intractable. A popular approach to improving the poor acceptance rate of the basic rejection sampling ABC algorithm is to use sequential Monte Carlo (ABC SMC) to produce a sequence of proposal distributions adapting towards the posterior, instead of generating values from the prior distribution of the model parameters. Proposal distribution for the subsequent iteration is typically obtained from a weighted set of samples, often called particles, of the current iteration of this sequence. Current methods for constructing these proposal distributions treat all the particles equivalently, regardless of the corresponding value generated by the sampler, which may lead to inefficiency when propagating the information across iterations of the algorithm. To improve sampler efficiency, we introduce a modified approach called stratified distance ABC SMC. Our algorithm stratifies particles based on their distance between the corresponding synthetic and observed data, and then constructs distinct proposal distributions for all the strata. Taking into account the distribution of distances across the particle space leads to substantially improved acceptance rate of the rejection sampling. We further show that efficiency can be gained by introducing a novel stopping rule for the sequential process based on the stratified posterior samples and demonstrate these advances by several examples.