In this paper we discuss several aspects of simulation based Bayesian econometric inference. We start at an elementary level on basic concepts of Bayesian analysis; evaluating integrals by simulation methods is a crucial ingredient in Bayesian inference. Next, the most popular and well-known simulation techniques are discussed, the Metropolis-Hastings algorithm and Gibbs sampling (being the most popular Markov chain Monte Carlo methods) and importance sampling. After that, we discuss two recently developed sampling methods: adaptive radial based direction sampling [ARDS], which makes use of a transformation to radial coordinates, and neural network sampling, which makes use of a neural network approximation to the posterior distribution of interest. Both methods are especially useful in cases where the posterior distribution is not well-behaved, in the sense of having highly non-elliptical shapes. The simulation techniques are illustrated in several example models, such as a model for the real US GNP and models for binary data of a US recession indicator.

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Persistent URL hdl.handle.net/1765/8523
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Hoogerheide, L.F., van Dijk, H.K., & van Oest, R.D.. (2007). Simulation based bayesian econometric inference: principles and some recent computational advances. (No. EI 2007-03). Report / Econometric Institute, Erasmus University Rotterdam. Retrieved from http://hdl.handle.net/1765/8523