For sufficiently nice regular, 1-dimensional Bayesian models, Edgeworth-type asymptotic expansions for the Bayesian posterior have been derived in
https://projecteuclid.org/journals/annals-of-mathematical-statistics/volume-41/issue-3/Asymptotic-Expansions-Associated-with-Posterior-Distributions/10.1214/aoms/1177696963.full
For sufficiently nice regular, 1-dimensional Bayesian models, Edgeworth-type asymptotic expansions for the Bayesian posterior have been derived in
https://projecteuclid.org/journals/annals-of-mathematical-statistics/volume-41/issue-3/Asymptotic-Expansions-Associated-with-Posterior-Distributions/10.1214/aoms/1177696963.full