Guided sequential ABC schemes for intractable Bayesian models

Preprint, 2023

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 high-dimensional summary statistics (180 summaries used to infer 21 parameters) and a simulation study of cell movements (using more than 400 summaries).