  This article tackles the old problem of prediction via a nonparametric
transformation model (NTM) in a new Bayesian way. Estimation of NTMs is known
challenging due to model unidentifiability though appealing because of its
robust prediction capability in survival analysis. Inspired by the uniqueness
of the posterior predictive distribution, we achieve efficient prediction via
the NTM aforementioned under the Bayesian paradigm. Our strategy is to assign
weakly informative priors to nonparametric components rather than identify the
model by adding complicated constraints in the existing literature. The
Bayesian success pays tribute to i) a subtle cast of NTMs by an exponential
transformation for the purpose of compressing spaces of infinite-dimensional
parameters to positive quadrants considering non-negativity of the failure
time; ii) a newly constructed weakly informative quantile-knots I-splines prior
for the recast transformation function together with the Dirichlet process
mixture model assigned to the error distribution. In addition, we provide a
convenient and precise estimator for the identified parameter component subject
to the general unit-norm restriction through posterior modification, enabling
effective relative risks. Simulations and applications on real datasets reveal
that our method is robust and outperforms the competing methods. An R package
BuLTM is available to predict survival curves, estimate relative risks, and
facilitate posterior checking.
