ABSTRACT
In stylized problems, conjugate prior distributions are available that allow for analytical solutions to finding posterior distributions. In most practical situations such conjugacy is either not available or overly restrictive and in order to evaluate the posterior model probabilities there are several computational matters that have to be considered. Posterior densities may be difficult or impossible to integrate explicitly, particularly when we have a complex model with many parameters. Markov Chain Monte Carlo can be complex to implement, and the results can be affected by the choice of starting values. The choice of proposal distribution can have a large impact on the convergence and acceptance rate of the Metropolis-Hastings algorithm. The Hamiltonian Monte Carlo is an alternative algorithm to Metropolis-Hastings and Gibbs sampling. The HMC can only be used to provide samples from continuous distributions in Rp.
