Abstract:  We present a class of transport-based algorithms to efficiently perform sequential Bayesian inference of static model parameters, in a setting where likelihood evaluations are not available or tractable. The strategy is based on the extraction of conditional distributions from the joint prior distribution of parameters and data, via the estimation of structured (e.g., block triangular) transport maps. We adapt this idea to the sequential setting via new recursive algorithms. To support near real-time applications with expensive models, we also discuss an offline/online approach that uses pre-computed maps to enable model-free computation during the online inference phase. The performance of these strategies will be illustrated on examples drawn from engineering applications.