4.5 Summary

In this chapter, we present the most popular methods for obtaining posterior draws when the posterior distribution does not have a standard closed-form solution. In particular, Markov chain Monte Carlo (MCMC) methods, such as Gibbs sampling and the Metropolis-Hastings algorithm, are the most commonly used approaches in this book. However, Hamiltonian Monte Carlo is gaining particular relevance in high-dimensional problems, while particle filtering (Sequential Monte Carlo) is widely applied in time series models.

Each problem requires careful consideration to determine the most appropriate method, and in many cases, a combination of methods is necessary. For instance, estimating fixed parameters in state-space models typically requires MCMC methods, while recursion of the state vector requires particle filtering. Additionally, convergence diagnostics are crucial because MCMC methods rely on technical assumptions that must be verified.