  Sequential algorithms such as sequential importance sampling (SIS) and
sequential Monte Carlo (SMC) have proven fundamental in Bayesian inference for
models not admitting a readily available likelihood function. For approximate
Bayesian computation (ABC), SMC-ABC is the state-of-art sampler. However, since
the ABC paradigm is intrinsically wasteful, sequential ABC schemes can benefit
from well-targeted proposal samplers that efficiently avoid improbable
parameter regions. We contribute to the ABC modeller's toolbox with novel
proposal samplers that are conditional to summary statistics of the data. In a
sense, the proposed parameters are "guided" to rapidly reach regions of the
posterior surface that are compatible with the observed data. This speeds up
the convergence of these sequential samplers, thus reducing the computational
effort, while preserving the accuracy in the inference. We provide a variety of
guided Gaussian and copula-based samplers for both SIS-ABC and SMC-ABC easing
inference for challenging case-studies, including multimodal posteriors, highly
correlated posteriors, hierarchical models with about 20 parameters, and a
simulation study of cell movements using more than 400 summary statistics.
