  Many applications in signal processing require the estimation of some
parameters of interest given a set of observed data. More specifically,
Bayesian inference needs the computation of {\it a-posteriori} estimators which
are often expressed as complicated multi-dimensional integrals. Unfortunately,
analytical expressions for these estimators cannot be found in most real-world
applications, and Monte Carlo methods are the only feasible approach. A very
powerful class of Monte Carlo techniques is formed by the Markov Chain Monte
Carlo (MCMC) algorithms. They generate a Markov chain such that its stationary
distribution coincides with the target posterior density. In this work, we
perform a thorough review of MCMC methods using multiple candidates in order to
select the next state of the chain, at each iteration. With respect to the
classical Metropolis-Hastings method, the use of multiple try techniques foster
the exploration of the sample space. We present different Multiple Try
Metropolis schemes, Ensemble MCMC methods, Particle Metropolis-Hastings
algorithms and the Delayed Rejection Metropolis technique. We highlight
limitations, benefits, connections and differences among the different methods,
and compare them by numerical simulations.
