  Typical Bayesian inference requires parameter identification via likelihood
parameterization, which has invited criticism for being less flexible than the
Frequentist framework and subject to misspecification. Though misspecification
may be avoided by functional parameter inference under a nonparametric model
space, there does not exist a flexible Bayesian semiparametric model that would
allow full control over the marginal prior over any general functional
parameter. We present the technique of $\theta$-augmentation which helps us
manipulate nonparametric models into semiparametric ones that directly target
any functional parameter. The method allows Bayesian probabilistic statements
to be drawn for any estimator that is defined as a functional of the empirical
distribution without requiring a likelihood function, thus providing a path to
Bayesian analysis in problems like causal inference and censoring where there
do not exist well-accepted likelihood functions.
