An asymptotic justification of the Bayesian bootstrap is given. Large-sample Bayesian bootstrap probability intervals for the mean, the variance and bands for the distribution, the smoothed density and smoothed rate function are also provided.
"A Large Sample Study of the Bayesian Bootstrap." Ann. Statist. 15 (1) 360 - 375, March, 1987. https://doi.org/10.1214/aos/1176350271