  We propose a sequential Monte Carlo (SMC) method to efficiently and
accurately compute cut-Bayesian posterior quantities of interest, variations of
standard Bayesian approaches constructed primarily to account for model
misspecification. We prove finite sample concentration bounds for estimators
derived from the proposed method along with a linear tempering extension and
apply these results to a realistic setting where a computer model is
misspecified. We then illustrate the SMC method for inference in a modular
chemical reactor example that includes submodels for reaction kinetics,
turbulence, mass transfer, and diffusion. The samples obtained are commensurate
with a direct-sampling approach that consists of running multiple Markov
chains, with computational efficiency gains using the SMC method. Overall, the
SMC method presented yields a novel, rigorous approach to computing with
cut-Bayesian posterior distributions.
