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Simulation based bayesian econometric inference: principles and some recent computational advances.
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Abstract
In this paper we discuss several aspects of simulation basedBayesian econometric inference. We start at an elementary level on basic concepts of Bayesian analysis; evaluatingintegrals by simulation methods is a crucial ingredientin Bayesian inference. Next, the most popular and well-knownsimulation techniques are discussed, the Metropolis-Hastingsalgorithm and Gibbs sampling (being the most popular Markovchain Monte Carlo methods) and importance sampling. After that, we discuss two recently developed samplingmethods: 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 ofinterest. Both methods are especially useful in cases wherethe posterior distribution is not well-behaved, in the senseof having highly non-elliptical shapes. The simulationtechniques are illustrated in several example models, suchas a model for the real US GNP and models for binary data ofa US recession indicator.