  Estimating model parameters of a general family of cure models is always a
challenging task mainly due to flatness and multimodality of the likelihood
function. In this work, we propose a fully Bayesian approach in order to
overcome these issues. Posterior inference is carried out by constructing a
Metropolis-coupled Markov chain Monte Carlo (MCMC) sampler, which combines
Gibbs sampling for the latent cure indicators and Metropolis-Hastings steps
with Langevin diffusion dynamics for parameter updates. The main MCMC algorithm
is embedded within a parallel tempering scheme by considering heated versions
of the target posterior distribution. It is demonstrated via simulations that
the proposed algorithm freely explores the multimodal posterior distribution
and produces robust point estimates, while it outperforms maximum likelihood
estimation via the Expectation-Maximization algorithm. A by-product of our
Bayesian implementation is to control the False Discovery Rate when classifying
items as cured or not. Finally, the proposed method is illustrated in a real
dataset which refers to recidivism for offenders released from prison; the
event of interest is whether the offender was re-incarcerated after probation
or not.
